LMFDB - Embedded newform 72.8.l.b.11.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,8,Mod(11,72)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("72.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	72.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$22.4917218349$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$80$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.10
Character	$\chi$	$=$	72.11
Dual form			72.8.l.b.59.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.4600 - 4.31154i) q^{2} +(41.7723 + 21.0255i) q^{3} +(90.8212 + 90.1971i) q^{4} +(-194.007 - 336.030i) q^{5} +(-346.284 - 400.029i) q^{6} +(-965.318 - 557.326i) q^{7} +(-561.096 - 1335.04i) q^{8} +(1302.86 + 1756.57i) q^{9} +O(q^{10})$	\(q+(-10.4600 - 4.31154i) q^{2} +(41.7723 + 21.0255i) q^{3} +(90.8212 + 90.1971i) q^{4} +(-194.007 - 336.030i) q^{5} +(-346.284 - 400.029i) q^{6} +(-965.318 - 557.326i) q^{7} +(-561.096 - 1335.04i) q^{8} +(1302.86 + 1756.57i) q^{9} +(580.496 + 4351.33i) q^{10} +(3100.96 + 1790.34i) q^{11} +(1897.38 + 5677.30i) q^{12} +(-2089.68 + 1206.48i) q^{13} +(7694.24 + 9991.62i) q^{14} +(-1038.93 - 18115.8i) q^{15} +(112.971 + 16383.6i) q^{16} -1028.84i q^{17} +(-6054.30 - 23990.9i) q^{18} -31452.9 q^{19} +(12689.0 - 48017.5i) q^{20} +(-28605.5 - 43577.1i) q^{21} +(-24716.8 - 32096.8i) q^{22} +(39883.9 + 69081.0i) q^{23} +(4631.49 - 67564.9i) q^{24} +(-36214.9 + 62726.0i) q^{25} +(27059.7 - 3609.95i) q^{26} +(17490.7 + 100769. i) q^{27} +(-37402.1 - 137686. i) q^{28} +(-29679.2 + 51405.8i) q^{29} +(-67240.1 + 193970. i) q^{30} +(-108688. + 62751.0i) q^{31} +(69457.0 - 171859. i) q^{32} +(91891.6 + 139986. i) q^{33} +(-4435.90 + 10761.6i) q^{34} +432501. i q^{35} +(-40110.3 + 277048. i) q^{36} -46161.9i q^{37} +(328996. + 135610. i) q^{38} +(-112658. + 6460.84i) q^{39} +(-339756. + 447552. i) q^{40} +(210680. - 121636. i) q^{41} +(111328. + 579148. i) q^{42} +(-454213. + 786720. i) q^{43} +(120149. + 442298. i) q^{44} +(337496. - 778585. i) q^{45} +(-119338. - 894545. i) q^{46} +(-526126. + 911277. i) q^{47} +(-339754. + 686757. i) q^{48} +(209454. + 362785. i) q^{49} +(649252. - 499969. i) q^{50} +(21631.9 - 42977.2i) q^{51} +(-298608. - 78909.4i) q^{52} -1.96747e6 q^{53} +(251519. - 1.12945e6i) q^{54} -1.38935e6i q^{55} +(-202415. + 1.60145e6i) q^{56} +(-1.31386e6 - 661312. i) q^{57} +(532081. - 409739. i) q^{58} +(-57759.7 + 33347.6i) q^{59} +(1.53964e6 - 1.73901e6i) q^{60} +(2.70106e6 + 1.55946e6i) q^{61} +(1.40742e6 - 187760. i) q^{62} +(-278689. - 2.42176e6i) q^{63} +(-1.46749e6 + 1.49817e6i) q^{64} +(810825. + 468130. i) q^{65} +(-357626. - 1.86044e6i) q^{66} +(-664708. - 1.15131e6i) q^{67} +(92798.6 - 93440.7i) q^{68} +(213583. + 3.72425e6i) q^{69} +(1.86475e6 - 4.52394e6i) q^{70} +4.15499e6 q^{71} +(1.61405e6 - 2.72497e6i) q^{72} -4.77155e6 q^{73} +(-199029. + 482851. i) q^{74} +(-2.83163e6 + 1.85878e6i) q^{75} +(-2.85659e6 - 2.83696e6i) q^{76} +(-1.99561e6 - 3.45649e6i) q^{77} +(1.20625e6 + 418148. i) q^{78} +(-3.86860e6 - 2.23354e6i) q^{79} +(5.48347e6 - 3.21650e6i) q^{80} +(-1.38809e6 + 4.57712e6i) q^{81} +(-2.72814e6 + 363952. i) q^{82} +(5.84310e6 + 3.37351e6i) q^{83} +(1.33254e6 - 6.53786e6i) q^{84} +(-345722. + 199603. i) q^{85} +(8.14303e6 - 6.27070e6i) q^{86} +(-2.32060e6 + 1.52332e6i) q^{87} +(650232. - 5.14445e6i) q^{88} +2.74961e6i q^{89} +(-6.88710e6 + 6.68884e6i) q^{90} +2.68961e6 q^{91} +(-2.60860e6 + 9.87143e6i) q^{92} +(-5.85952e6 + 336039. i) q^{93} +(9.43226e6 - 7.26349e6i) q^{94} +(6.10208e6 + 1.05691e7i) q^{95} +(6.51480e6 - 5.71858e6i) q^{96} +(-3.42583e6 + 5.93371e6i) q^{97} +(-626715. - 4.69778e6i) q^{98} +(895255. + 7.77961e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9}+O(q^{10}) $ 160 * q - 3 * q^2 - 90 * q^3 - 257 * q^4 - 459 * q^6 + 3018 * q^9	\( 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9} + 252 q^{10} - 26448 q^{11} - 27234 q^{12} - 43488 q^{14} + 32767 q^{16} + 21762 q^{18} - 119452 q^{19} + 130806 q^{20} - 6049 q^{22} - 83379 q^{24} - 1312502 q^{25} - 94428 q^{27} - 32772 q^{28} + 735060 q^{30} + 308907 q^{32} - 1249812 q^{33} - 188203 q^{34} - 1410345 q^{36} + 353415 q^{38} - 477876 q^{40} - 1612476 q^{41} - 39360 q^{42} + 220508 q^{43} + 1082496 q^{46} - 3515619 q^{48} + 9882514 q^{49} - 136947 q^{50} - 2358786 q^{51} + 1089018 q^{52} - 8083005 q^{54} - 1285266 q^{56} - 2070294 q^{57} + 1295022 q^{58} - 8748744 q^{59} - 3070044 q^{60} + 16058050 q^{64} - 6 q^{65} - 19546374 q^{66} + 3851300 q^{67} + 10545975 q^{68} + 979920 q^{70} + 12593427 q^{72} - 9731236 q^{73} + 13246572 q^{74} + 8347746 q^{75} - 4009903 q^{76} - 9123732 q^{78} - 6855198 q^{81} + 21020522 q^{82} - 14348826 q^{83} + 44644836 q^{84} + 80099985 q^{86} + 10463891 q^{88} + 7437678 q^{90} - 3294180 q^{91} - 57890184 q^{92} - 1609122 q^{94} + 69780834 q^{96} + 9938888 q^{97} - 16049670 q^{99}+O(q^{100}) \) 160 * q - 3 * q^2 - 90 * q^3 - 257 * q^4 - 459 * q^6 + 3018 * q^9 + 252 * q^10 - 26448 * q^11 - 27234 * q^12 - 43488 * q^14 + 32767 * q^16 + 21762 * q^18 - 119452 * q^19 + 130806 * q^20 - 6049 * q^22 - 83379 * q^24 - 1312502 * q^25 - 94428 * q^27 - 32772 * q^28 + 735060 * q^30 + 308907 * q^32 - 1249812 * q^33 - 188203 * q^34 - 1410345 * q^36 + 353415 * q^38 - 477876 * q^40 - 1612476 * q^41 - 39360 * q^42 + 220508 * q^43 + 1082496 * q^46 - 3515619 * q^48 + 9882514 * q^49 - 136947 * q^50 - 2358786 * q^51 + 1089018 * q^52 - 8083005 * q^54 - 1285266 * q^56 - 2070294 * q^57 + 1295022 * q^58 - 8748744 * q^59 - 3070044 * q^60 + 16058050 * q^64 - 6 * q^65 - 19546374 * q^66 + 3851300 * q^67 + 10545975 * q^68 + 979920 * q^70 + 12593427 * q^72 - 9731236 * q^73 + 13246572 * q^74 + 8347746 * q^75 - 4009903 * q^76 - 9123732 * q^78 - 6855198 * q^81 + 21020522 * q^82 - 14348826 * q^83 + 44644836 * q^84 + 80099985 * q^86 + 10463891 * q^88 + 7437678 * q^90 - 3294180 * q^91 - 57890184 * q^92 - 1609122 * q^94 + 69780834 * q^96 + 9938888 * q^97 - 16049670 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−10.4600	−	4.31154i	−0.924538	−	0.381090i
$2$	−10.4600	−	4.31154i	−0.924538	−	0.381090i
$3$	41.7723	+	21.0255i	0.893232	+	0.449595i
$3$	41.7723	+	21.0255i	0.893232	+	0.449595i
$4$	90.8212	+	90.1971i	0.709540	+	0.704665i
$5$	−194.007	−	336.030i	−0.694100	−	1.20222i	−0.970483	−	0.241169i	$-0.922469\pi$
$5$	−194.007	−	336.030i	−0.694100	−	1.20222i	0.276383	−	0.961048i	$-0.410864\pi$
$6$	−346.284	−	400.029i	−0.654491	−	0.756070i
$7$	−965.318	−	557.326i	−1.06372	−	0.614139i	−0.137261	−	0.990535i	$-0.543830\pi$
$7$	−965.318	−	557.326i	−1.06372	−	0.614139i	−0.926459	+	0.376396i	$0.877163\pi$
$8$	−561.096	−	1335.04i	−0.387456	−	0.921888i
$9$	1302.86	+	1756.57i	0.595728	+	0.803186i
$10$	580.496	+	4351.33i	0.183569	+	1.37601i
$11$	3100.96	+	1790.34i	0.702460	+	0.405566i	0.808263	−	0.588821i	$-0.200408\pi$
$11$	3100.96	+	1790.34i	0.702460	+	0.405566i	−0.105803	+	0.994387i	$0.533741\pi$
$12$	1897.38	+	5677.30i	0.316971	+	0.948435i
$13$	−2089.68	+	1206.48i	−0.263802	+	0.152306i	−0.626068	−	0.779769i	$-0.715337\pi$
$13$	−2089.68	+	1206.48i	−0.263802	+	0.152306i	0.362266	+	0.932075i	$0.382003\pi$
$14$	7694.24	+	9991.62i	0.749407	+	0.973168i
$15$	−1038.93	−	18115.8i	−0.0794818	−	1.38592i
$16$	112.971	+	16383.6i	0.00689522	+	0.999976i
$17$		−	1028.84i		−	0.0507899i	−0.999677	−	0.0253950i	$-0.991916\pi$
$17$		−	1028.84i		−	0.0507899i	0.999677	−	0.0253950i	$-0.00808434\pi$
$18$	−6054.30	−	23990.9i	−0.244687	−	0.969602i
$19$	−31452.9			−1.05202			−0.526009	−	0.850479i	$-0.676312\pi$
$19$	−31452.9			−1.05202			−0.526009	+	0.850479i	$0.676312\pi$
$20$	12689.0	−	48017.5i	0.354668	−	1.34213i
$21$	−28605.5	−	43577.1i	−0.674035	−	1.02681i
$22$	−24716.8	−	32096.8i	−0.494894	−	0.642662i
$23$	39883.9	+	69081.0i	0.683519	+	1.18389i	0.973900	+	0.226978i	$0.0728846\pi$
$23$	39883.9	+	69081.0i	0.683519	+	1.18389i	−0.290381	+	0.956911i	$0.593782\pi$
$24$	4631.49	−	67564.9i	0.0683883	−	0.997659i
$25$	−36214.9	+	62726.0i	−0.463551	+	0.802893i
$26$	27059.7	−	3609.95i	0.301937	−	0.0402804i
$27$	17490.7	+	100769.i	0.171015	+	0.985268i
$28$	−37402.1	−	137686.i	−0.321990	−	1.18532i
$29$	−29679.2	+	51405.8i	−0.225974	+	0.391399i	−0.956611	−	0.291367i	$-0.905890\pi$
$29$	−29679.2	+	51405.8i	−0.225974	+	0.391399i	0.730637	+	0.682766i	$0.239223\pi$
$30$	−67240.1	+	193970.i	−0.454678	+	1.31163i
$31$	−108688.	+	62751.0i	−0.655262	+	0.378316i	−0.790469	−	0.612502i	$-0.790163\pi$
$31$	−108688.	+	62751.0i	−0.655262	+	0.378316i	0.135207	+	0.990817i	$0.456830\pi$
$32$	69457.0	−	171859.i	0.374706	−	0.927144i
$33$	91891.6	+	139986.i	0.445120	+	0.678087i
$34$	−4435.90	+	10761.6i	−0.0193555	+	0.0469572i
$35$			432501.i			1.70510i
$36$	−40110.3	+	277048.i	−0.143284	+	0.989682i
$37$		−	46161.9i		−	0.149823i	−0.997190	−	0.0749113i	$-0.976133\pi$
$37$		−	46161.9i		−	0.149823i	0.997190	−	0.0749113i	$-0.0238674\pi$
$38$	328996.	+	135610.i	0.972630	+	0.400914i
$39$	−112658.	+	6460.84i	−0.304113	+	0.0174406i
$40$	−339756.	+	447552.i	−0.839376	+	1.10569i
$41$	210680.	−	121636.i	0.477396	−	0.275625i	−0.241934	−	0.970293i	$-0.577782\pi$
$41$	210680.	−	121636.i	0.477396	−	0.275625i	0.719331	+	0.694668i	$0.244449\pi$
$42$	111328.	+	579148.i	0.231863	+	1.20619i
$43$	−454213.	+	786720.i	−0.871204	+	1.50897i	−0.0104528	+	0.999945i	$0.503327\pi$
$43$	−454213.	+	786720.i	−0.871204	+	1.50897i	−0.860752	+	0.509025i	$0.830006\pi$
$44$	120149.	+	442298.i	0.212636	+	0.782764i
$45$	337496.	−	778585.i	0.552109	−	1.27369i
$46$	−119338.	−	894545.i	−0.180770	−	1.35503i
$47$	−526126.	+	911277.i	−0.739175	+	1.28029i	0.213693	+	0.976901i	$0.431451\pi$
$47$	−526126.	+	911277.i	−0.739175	+	1.28029i	−0.952867	+	0.303387i	$0.901882\pi$
$48$	−339754.	+	686757.i	−0.443426	+	0.896311i
$49$	209454.	+	362785.i	0.254333	+	0.440517i
$50$	649252.	−	499969.i	0.734545	−	0.565650i
$51$	21631.9	−	42977.2i	0.0228349	−	0.0453672i
$52$	−298608.	−	78909.4i	−0.294503	−	0.0778246i
$53$	−1.96747e6			−1.81527			−0.907636	−	0.419757i	$-0.862115\pi$
$53$	−1.96747e6			−1.81527			−0.907636	+	0.419757i	$0.862115\pi$
$54$	251519.	−	1.12945e6i	0.217366	−	0.976090i
$55$		−	1.38935e6i		−	1.12601i
$56$	−202415.	+	1.60145e6i	−0.154023	+	1.21858i
$57$	−1.31386e6	−	661312.i	−0.939696	−	0.472982i
$58$	532081.	−	409739.i	0.358080	−	0.275746i
$59$	−57759.7	+	33347.6i	−0.0366136	+	0.0211389i	−0.518195	−	0.855262i	$-0.673396\pi$
$59$	−57759.7	+	33347.6i	−0.0366136	+	0.0211389i	0.481581	+	0.876401i	$0.340063\pi$
$60$	1.53964e6	−	1.73901e6i	0.920216	−	1.03938i
$61$	2.70106e6	+	1.55946e6i	1.52363	+	0.879670i	0.999609	+	0.0279671i	$0.00890335\pi$
$61$	2.70106e6	+	1.55946e6i	1.52363	+	0.879670i	0.524025	+	0.851703i	$0.324430\pi$
$62$	1.40742e6	−	187760.i	0.749987	−	0.100053i
$63$	−278689.	−	2.42176e6i	−0.140420	−	1.22022i
$64$	−1.46749e6	+	1.49817e6i	−0.699756	+	0.714382i
$65$	810825.	+	468130.i	0.366210	+	0.211431i
$66$	−357626.	−	1.86044e6i	−0.153118	−	0.796548i
$67$	−664708.	−	1.15131e6i	−0.270003	−	0.467659i	0.698859	−	0.715259i	$-0.253691\pi$
$67$	−664708.	−	1.15131e6i	−0.270003	−	0.467659i	−0.968862	+	0.247600i	$0.920358\pi$
$68$	92798.6	−	93440.7i	0.0357899	−	0.0360375i
$69$	213583.	+	3.72425e6i	0.0782701	+	1.36480i
$70$	1.86475e6	−	4.52394e6i	0.649795	−	1.57643i
$71$	4.15499e6			1.37773			0.688867	−	0.724888i	$-0.258108\pi$
$71$	4.15499e6			1.37773			0.688867	+	0.724888i	$0.258108\pi$
$72$	1.61405e6	−	2.72497e6i	0.509629	−	0.860394i
$73$	−4.77155e6			−1.43559			−0.717793	−	0.696256i	$-0.754848\pi$
$73$	−4.77155e6			−1.43559			−0.717793	+	0.696256i	$0.754848\pi$
$74$	−199029.	+	482851.i	−0.0570959	+	0.138517i
$75$	−2.83163e6	+	1.85878e6i	−0.775035	+	0.508760i
$76$	−2.85659e6	−	2.83696e6i	−0.746449	−	0.741319i
$77$	−1.99561e6	−	3.45649e6i	−0.498147	−	0.862816i
$78$	1.20625e6	+	418148.i	0.287810	+	0.0997698i
$79$	−3.86860e6	−	2.23354e6i	−0.882794	−	0.509681i	−0.0112154	−	0.999937i	$-0.503570\pi$
$79$	−3.86860e6	−	2.23354e6i	−0.882794	−	0.509681i	−0.871579	+	0.490256i	$0.836903\pi$
$80$	5.48347e6	−	3.21650e6i	1.19740	−	0.702373i
$81$	−1.38809e6	+	4.57712e6i	−0.290216	+	0.956961i
$82$	−2.72814e6	+	363952.i	−0.546409	+	0.0728946i
$83$	5.84310e6	+	3.37351e6i	1.12168	+	0.647604i	0.941830	−	0.336090i	$-0.109105\pi$
$83$	5.84310e6	+	3.37351e6i	1.12168	+	0.647604i	0.179853	+	0.983694i	$0.442438\pi$
$84$	1.33254e6	−	6.53786e6i	0.245303	−	1.20353i
$85$	−345722.	+	199603.i	−0.0610605	+	0.0352533i
$86$	8.14303e6	−	6.27070e6i	1.38052	−	1.06309i
$87$	−2.32060e6	+	1.52332e6i	−0.377818	+	0.248013i
$88$	650232.	−	5.14445e6i	0.101714	−	0.804729i
$89$			2.74961e6i			0.413434i	0.978401	+	0.206717i	$0.0662779\pi$
$89$			2.74961e6i			0.413434i	−0.978401	+	0.206717i	$0.933722\pi$
$90$	−6.88710e6	+	6.68884e6i	−0.995835	+	0.967168i
$91$	2.68961e6			0.374148
$92$	−2.60860e6	+	9.87143e6i	−0.349261	+	1.32167i
$93$	−5.85952e6	+	336039.i	−0.755390	+	0.0433211i
$94$	9.43226e6	−	7.26349e6i	1.17130	−	0.901983i
$95$	6.10208e6	+	1.05691e7i	0.730206	+	1.26475i
$96$	6.51480e6	−	5.71858e6i	0.751539	−	0.659688i
$97$	−3.42583e6	+	5.93371e6i	−0.381123	+	0.660124i	−0.991223	−	0.132200i	$-0.957796\pi$
$97$	−3.42583e6	+	5.93371e6i	−0.381123	+	0.660124i	0.610100	+	0.792324i	$0.291129\pi$
$98$	−626715.	−	4.69778e6i	−0.0672634	−	0.504198i
$99$	895255.	+	7.77961e6i	0.0927307	+	0.805813i
$100$	−8.94678e6	+	2.43037e6i	−0.894678	+	0.243037i
$101$	4.04822e6	−	7.01172e6i	0.390966	−	0.677173i	−0.601611	−	0.798789i	$-0.705474\pi$
$101$	4.04822e6	−	7.01172e6i	0.390966	−	0.677173i	0.992577	+	0.121616i	$0.0388077\pi$
$102$	−411567.	+	356272.i	−0.0384007	+	0.0332415i
$103$	−8.26351e6	+	4.77094e6i	−0.745134	+	0.430203i	−0.823933	−	0.566687i	$-0.808225\pi$
$103$	−8.26351e6	+	4.77094e6i	−0.745134	+	0.430203i	0.0787991	+	0.996891i	$0.474891\pi$
$104$	2.78320e6	+	2.11285e6i	0.242621	+	0.184184i
$105$	−9.09354e6	+	1.80666e7i	−0.766603	+	1.52305i
$106$	2.05796e7	+	8.48282e6i	1.67829	+	0.691783i
$107$		−	2.12974e7i		−	1.68067i	−0.542066	−	0.840336i	$-0.682358\pi$
$107$		−	2.12974e7i		−	1.68067i	0.542066	−	0.840336i	$-0.317642\pi$
$108$	−7.50056e6	+	1.07296e7i	−0.572942	+	0.819596i
$109$		−	2.13414e7i		−	1.57845i	−0.614106	−	0.789224i	$-0.710483\pi$
$109$		−	2.13414e7i		−	1.57845i	0.614106	−	0.789224i	$-0.289517\pi$
$110$	−5.99026e6	+	1.45326e7i	−0.429113	+	1.04104i
$111$	970576.	−	1.92829e6i	0.0673595	−	0.133826i
$112$	9.02196e6	−	1.58783e7i	0.606789	−	1.06793i
$113$	−5.77672e6	+	3.33519e6i	−0.376623	+	0.217443i	−0.676348	−	0.736582i	$-0.736438\pi$
$113$	−5.77672e6	+	3.33519e6i	−0.376623	+	0.217443i	0.299725	+	0.954026i	$0.403105\pi$
$114$	1.08916e7	+	1.25821e7i	0.688536	+	0.795399i
$115$	1.54755e7	−	2.68044e7i	0.948861	−	1.64348i
$116$	−7.33215e6	+	1.99176e6i	−0.436142	+	0.118477i
$117$	−4.84181e6	−	2.09880e6i	−0.279484	−	0.121149i
$118$	747943.	−	99780.5i	0.0419065	−	0.00559060i
$119$	−573401.	+	993159.i	−0.0311921	+	0.0540262i
$120$	−2.36024e7	+	1.15517e7i	−1.24687	+	0.610258i
$121$	−3.33295e6	−	5.77283e6i	−0.171033	−	0.296238i
$122$	−2.15293e7	−	2.79576e7i	−1.07342	−	1.39393i
$123$	1.13580e7	−	651376.i	0.550346	−	0.0315619i
$124$	−1.55311e7	−	4.10421e6i	−0.731521	−	0.193310i
$125$	−2.20983e6			−0.101198
$126$	−7.52646e6	+	2.65331e7i	−0.335192	+	1.18166i
$127$			1.38149e7i			0.598461i	0.954181	+	0.299231i	$0.0967300\pi$
$127$			1.38149e7i			0.598461i	−0.954181	+	0.299231i	$0.903270\pi$
$128$	2.18093e7	−	9.34361e6i	0.919195	−	0.393804i
$129$	−3.55147e7	+	2.33131e7i	−1.45661	+	0.956172i
$130$	−6.46283e6	−	8.39252e6i	−0.258001	−	0.335036i
$131$	2.47727e7	−	1.43025e7i	0.962773	−	0.555857i	0.0657477	−	0.997836i	$-0.479057\pi$
$131$	2.47727e7	−	1.43025e7i	0.962773	−	0.555857i	0.897025	+	0.441979i	$0.145723\pi$
$132$	−4.28062e6	+	2.10020e7i	−0.161994	+	0.794791i
$133$	3.03620e7	+	1.75295e7i	1.11905	+	0.646084i
$134$	1.98890e6	+	1.49085e7i	0.0714078	+	0.535264i
$135$	3.04681e7	−	2.54273e7i	1.06580	−	0.889472i
$136$	−1.37354e6	+	577280.i	−0.0468226	+	0.0196789i
$137$	−1.18662e7	−	6.85092e6i	−0.394265	−	0.227629i	0.289742	−	0.957105i	$-0.406431\pi$
$137$	−1.18662e7	−	6.85092e6i	−0.394265	−	0.227629i	−0.684006	+	0.729476i	$0.739764\pi$
$138$	1.38232e7	−	3.98764e7i	0.447747	−	1.29163i
$139$	−5.14990e6	−	8.91989e6i	−0.162647	−	0.281714i	0.773170	−	0.634199i	$-0.218670\pi$
$139$	−5.14990e6	−	8.91989e6i	−0.162647	−	0.281714i	−0.935817	+	0.352485i	$0.885337\pi$
$140$	−3.90103e7	+	3.92802e7i	−1.20152	+	1.20983i
$141$	−4.11375e7	+	2.70041e7i	−1.23587	+	0.811265i
$142$	−4.34609e7	−	1.79144e7i	−1.27377	−	0.525041i
$143$	−8.64002e6			−0.247081
$144$	−2.86317e7	+	2.15440e7i	−0.799059	+	0.601252i
$145$	2.30318e7			0.627395
$146$	4.99102e7	+	2.05727e7i	1.32725	+	0.547088i
$147$	1.12165e6	+	1.95582e7i	0.0291237	+	0.507831i
$148$	4.16367e6	−	4.19247e6i	0.105575	−	0.106305i
$149$	2.51935e7	+	4.36364e7i	0.623930	+	1.08068i	0.988747	+	0.149600i	$0.0477985\pi$
$149$	2.51935e7	+	4.36364e7i	0.623930	+	1.08068i	−0.364816	+	0.931080i	$0.618868\pi$
$150$	3.76329e7	−	7.23404e6i	0.910433	−	0.175009i
$151$	4.17853e7	+	2.41247e7i	0.987652	+	0.570221i	0.904572	−	0.426322i	$-0.140191\pi$
$151$	4.17853e7	+	2.41247e7i	0.987652	+	0.570221i	0.0830803	+	0.996543i	$0.473524\pi$
$152$	1.76481e7	+	4.19908e7i	0.407610	+	0.969842i
$153$	1.80723e6	−	1.34043e6i	0.0407938	−	0.0302570i
$154$	5.97113e6	+	4.47589e7i	0.131745	+	0.987545i
$155$	4.21724e7	+	2.43482e7i	0.909635	+	0.525178i
$156$	−1.08144e7	−	9.57461e6i	−0.228070	−	0.201923i
$157$	−4.08465e7	+	2.35827e7i	−0.842375	+	0.486346i	−0.858071	−	0.513531i	$-0.828337\pi$
$157$	−4.08465e7	+	2.35827e7i	−0.842375	+	0.486346i	0.0156955	+	0.999877i	$0.495004\pi$
$158$	3.08354e7	+	4.00424e7i	0.621942	+	0.807644i
$159$	−8.21857e7	−	4.13670e7i	−1.62146	−	0.816138i
$160$	−7.12248e7	+	1.00022e7i	−1.37471	+	0.193052i
$161$		−	8.89135e7i		−	1.67910i
$162$	3.42538e7	−	4.18916e7i	0.633004	−	0.774148i
$163$	9.77079e7			1.76715			0.883574	−	0.468291i	$-0.155130\pi$
$163$	9.77079e7			1.76715			0.883574	+	0.468291i	$0.155130\pi$
$164$	3.01054e7	+	7.95557e6i	0.532955	+	0.140837i
$165$	2.92118e7	−	5.80366e7i	0.506250	−	1.00579i
$166$	−4.65735e7	−	6.04796e7i	−0.790242	−	1.02620i
$167$	−3.97207e7	−	6.87984e7i	−0.659948	−	1.14306i	−0.980629	−	0.195876i	$-0.937245\pi$
$167$	−3.97207e7	−	6.87984e7i	−0.659948	−	1.14306i	0.320681	−	0.947187i	$-0.396088\pi$
$168$	−4.21266e7	+	6.26404e7i	−0.685447	+	1.01923i
$169$	−2.84631e7	+	4.92995e7i	−0.453606	+	0.785668i
$170$	4.47683e6	−	597238.i	0.0698874	−	0.00932345i
$171$	−4.09786e7	−	5.52491e7i	−0.626716	−	0.844966i
$172$	−1.12212e8	+	3.04822e7i	−1.68147	+	0.456768i
$173$	−448087.	+	776109.i	−0.00657962	+	0.0113962i	−0.869296	−	0.494291i	$-0.835428\pi$
$173$	−448087.	+	776109.i	−0.00657962	+	0.0113962i	0.862717	+	0.505687i	$0.168761\pi$
$174$	3.08412e7	−	5.92851e6i	0.443823	−	0.0853145i
$175$	6.99177e7	−	4.03670e7i	0.986175	−	0.569369i
$176$	−2.89819e7	+	5.10072e7i	−0.400712	+	0.705240i
$177$	−3.11391e6	+	178580.i	−0.0422084	+	0.00242062i
$178$	1.18551e7	−	2.87608e7i	0.157556	−	0.382235i
$179$		−	1.48430e8i		−	1.93436i	−0.254092	−	0.967180i	$-0.581777\pi$
$179$		−	1.48430e8i		−	1.93436i	0.254092	−	0.967180i	$-0.418223\pi$
$180$	1.00878e8	−	4.02709e7i	1.28927	−	0.514680i
$181$		−	2.64608e7i		−	0.331686i	−0.986152	−	0.165843i	$-0.946965\pi$
$181$		−	2.64608e7i		−	0.331686i	0.986152	−	0.165843i	$-0.0530345\pi$
$182$	−2.81332e7	−	1.15964e7i	−0.345914	−	0.142584i
$183$	8.00414e7	+	1.21934e8i	0.965463	+	1.47077i
$184$	6.98469e7	−	9.20076e7i	0.826580	−	1.08883i
$185$	−1.55118e7	+	8.95572e6i	−0.180119	+	0.103992i
$186$	6.27391e7	+	2.17486e7i	0.714896	+	0.247820i
$187$	1.84198e6	−	3.19040e6i	0.0205987	−	0.0356779i
$188$	−1.29978e8	+	3.53082e7i	−1.42665	+	0.387546i
$189$	3.92772e7	−	1.07022e8i	0.423180	−	1.15308i
$190$	−1.82583e7	−	1.36862e8i	−0.193118	−	1.44759i
$191$	−5.94197e7	+	1.02918e8i	−0.617040	+	1.06875i	0.372983	+	0.927838i	$0.378335\pi$
$191$	−5.94197e7	+	1.02918e8i	−0.617040	+	1.06875i	−0.990023	+	0.140907i	$0.954998\pi$
$192$	−9.28004e7	+	3.17272e7i	−0.946227	+	0.323503i
$193$	3.81627e6	+	6.60998e6i	0.0382110	+	0.0661835i	0.884498	−	0.466543i	$-0.154501\pi$
$193$	3.81627e6	+	6.60998e6i	0.0382110	+	0.0661835i	−0.846287	+	0.532727i	$0.821167\pi$
$194$	6.14175e7	−	4.72957e7i	0.603929	−	0.465067i
$195$	2.40274e7	+	3.66029e7i	0.232052	+	0.353504i
$196$	−1.36993e7	+	5.18407e7i	−0.129958	+	0.491784i
$197$	5.87710e7			0.547685			0.273843	−	0.961775i	$-0.411705\pi$
$197$	5.87710e7			0.547685			0.273843	+	0.961775i	$0.411705\pi$
$198$	2.41778e7	−	8.52342e7i	0.221355	−	0.780344i
$199$			7.05649e7i			0.634750i	0.948300	+	0.317375i	$0.102801\pi$
$199$			7.05649e7i			0.634750i	−0.948300	+	0.317375i	$0.897199\pi$
$200$	1.04062e8	+	1.31529e7i	0.919783	+	0.116256i
$201$	−3.55959e6	−	6.20686e7i	−0.0309182	−	0.539120i
$202$	−7.25755e7	+	5.58882e7i	−0.619527	+	0.477079i
$203$	5.72996e7	−	3.30820e7i	0.480746	−	0.277559i
$204$	5.84105e6	−	1.95210e6i	0.0481710	−	0.0160989i
$205$	−8.17467e7	−	4.71965e7i	−0.662722	−	0.382623i
$206$	1.07006e8	−	1.42753e7i	0.852851	−	0.113776i
$207$	−6.93824e7	+	1.60062e8i	−0.543692	+	1.25427i
$208$	−2.00025e7	−	3.41002e7i	−0.154121	−	0.262746i
$209$	−9.75342e7	−	5.63114e7i	−0.739000	−	0.426662i
$210$	1.73013e8	−	1.49768e8i	1.28917	−	1.11597i
$211$	3.33541e7	+	5.77709e7i	0.244433	+	0.423371i	0.961972	−	0.273148i	$-0.0880648\pi$
$211$	3.33541e7	+	5.77709e7i	0.244433	+	0.423371i	−0.717539	+	0.696518i	$0.754731\pi$
$212$	−1.78688e8	−	1.77460e8i	−1.28801	−	1.27916i
$213$	1.73563e8	+	8.73606e7i	1.23064	+	0.619423i
$214$	−9.18246e7	+	2.22770e8i	−0.640488	+	1.55384i
$215$	3.52482e8			2.41881
$216$	1.24717e8	−	7.98919e7i	0.842047	−	0.539405i
$217$	1.39891e8			0.929353
$218$	−9.20144e7	+	2.23230e8i	−0.601531	+	1.45933i
$219$	−1.99319e8	−	1.00324e8i	−1.28231	−	0.645433i
$220$	1.25316e8	−	1.26183e8i	0.793462	−	0.798952i
$221$	1.24127e6	+	2.14995e6i	0.00773562	+	0.0133985i
$222$	−1.84661e7	+	1.59851e7i	−0.113276	+	0.0980575i
$223$	−2.25634e8	−	1.30270e8i	−1.36250	−	0.786642i	−0.372548	−	0.928013i	$-0.621516\pi$
$223$	−2.25634e8	−	1.30270e8i	−1.36250	−	0.786642i	−0.989957	+	0.141371i	$0.954849\pi$
$224$	−1.62830e8	+	1.27188e8i	−0.967977	+	0.756099i
$225$	−1.57365e8	+	1.81092e7i	−0.921023	+	0.105989i
$226$	7.48040e7	−	9.97935e6i	0.431067	−	0.0575072i
$227$	−1.09207e8	−	6.30505e7i	−0.619668	−	0.357765i	0.157072	−	0.987587i	$-0.449795\pi$
$227$	−1.09207e8	−	6.30505e7i	−0.619668	−	0.357765i	−0.776740	+	0.629822i	$0.783128\pi$
$228$	−5.96779e7	−	1.78568e8i	−0.333458	−	0.997770i
$229$	−2.35630e8	+	1.36041e8i	−1.29660	+	0.748594i	−0.979816	−	0.199902i	$-0.935938\pi$
$229$	−2.35630e8	+	1.36041e8i	−1.29660	+	0.748594i	−0.316788	+	0.948496i	$0.602604\pi$
$230$	−2.77441e8	+	2.13649e8i	−1.50357	+	1.15785i
$231$	−1.06867e7	−	1.86345e8i	−0.0570431	−	0.994660i
$232$	8.52815e7	+	1.07792e7i	0.448381	+	0.0566730i
$233$		−	1.55115e8i		−	0.803358i	−0.915781	−	0.401679i	$-0.868427\pi$
$233$		−	1.55115e8i		−	0.803358i	0.915781	−	0.401679i	$-0.131573\pi$
$234$	4.15961e7	+	4.28290e7i	0.212225	+	0.218516i
$235$	4.08288e8			2.05225
$236$	−8.25365e6	−	2.18109e6i	−0.0408747	−	0.0108014i
$237$	−1.14639e8	−	1.74639e8i	−0.559390	−	0.852164i
$238$	1.02798e7	−	7.91616e6i	0.0494271	−	0.0380623i
$239$	−1.56355e8	−	2.70814e8i	−0.740830	−	1.28315i	−0.952118	−	0.305731i	$-0.901099\pi$
$239$	−1.56355e8	−	2.70814e8i	−0.740830	−	1.28315i	0.211288	−	0.977424i	$-0.432234\pi$
$240$	2.96686e8	−	1.90680e7i	1.38534	−	0.0890361i
$241$	−1.63336e8	+	2.82907e8i	−0.751662	+	1.30192i	0.195355	+	0.980733i	$0.437414\pi$
$241$	−1.63336e8	+	2.82907e8i	−0.751662	+	1.30192i	−0.947017	+	0.321184i	$0.895919\pi$
$242$	9.97264e6	+	7.47537e7i	0.0452331	+	0.339062i
$243$	−1.54220e8	+	1.62011e8i	−0.689476	+	0.724309i
$244$	1.04655e8	+	3.85260e8i	0.461207	+	1.69781i
$245$	8.12710e7	−	1.40765e8i	0.353065	−	0.611526i
$246$	−1.21613e8	−	4.21573e7i	−0.520843	−	0.180551i
$247$	6.57265e7	−	3.79472e7i	0.277524	−	0.160229i
$248$	1.44759e8	+	1.09893e8i	0.602650	+	0.457498i
$249$	1.73150e8	+	2.63774e8i	0.710764	+	1.08276i
$250$	2.31147e7	+	9.52776e6i	0.0935616	+	0.0385657i
$251$			3.02761e8i			1.20849i	0.796800	+	0.604243i	$0.206525\pi$
$251$			3.02761e8i			1.20849i	−0.796800	+	0.604243i	$0.793475\pi$
$252$	1.93125e8	−	2.45084e8i	0.760215	−	0.964747i
$253$			2.85623e8i			1.10885i
$254$	5.95637e7	−	1.44504e8i	0.228068	−	0.553300i
$255$	−1.86383e7	+	1.06890e6i	−0.0703909	+	0.00403687i
$256$	−2.68410e8	+	3.70175e6i	−0.999905	+	0.0137901i
$257$	−3.29060e8	+	1.89983e8i	−1.20923	+	0.698150i	−0.962591	−	0.270957i	$-0.912660\pi$
$257$	−3.29060e8	+	1.89983e8i	−1.20923	+	0.698150i	−0.246640	+	0.969107i	$0.579326\pi$
$258$	4.71998e8	−	9.07305e7i	1.71108	−	0.328916i
$259$	−2.57272e7	+	4.45609e7i	−0.0920118	+	0.159369i
$260$	3.14161e7	+	1.15650e8i	0.110853	+	0.408075i
$261$	−1.28966e8	+	1.48410e7i	−0.448985	+	0.0516679i
$262$	−3.20787e8	+	4.27951e7i	−1.10195	+	0.147008i
$263$	−5.30440e6	+	9.18749e6i	−0.0179801	+	0.0311424i	−0.874875	−	0.484348i	$-0.839057\pi$
$263$	−5.30440e6	+	9.18749e6i	−0.0179801	+	0.0311424i	0.856895	+	0.515490i	$0.172390\pi$
$264$	1.35326e8	−	2.01224e8i	0.452656	−	0.673080i
$265$	3.81702e8	+	6.61128e8i	1.25998	+	2.18235i
$266$	−2.42006e8	−	3.14265e8i	−0.788389	−	1.02379i
$267$	−5.78119e7	+	1.14858e8i	−0.185878	+	0.369292i
$268$	4.34750e7	−	1.64518e8i	0.137965	−	0.522085i
$269$	−2.53740e8			−0.794795			−0.397398	−	0.917646i	$-0.630087\pi$
$269$	−2.53740e8			−0.794795			−0.397398	+	0.917646i	$0.630087\pi$
$270$	−4.28326e8	+	1.34604e8i	−1.32435	+	0.416183i
$271$			3.07425e8i			0.938311i	0.883115	+	0.469156i	$0.155442\pi$
$271$			3.07425e8i			0.938311i	−0.883115	+	0.469156i	$0.844558\pi$
$272$	1.68562e7	−	116230.i	0.0507887	−	0.000350208i
$273$	1.12351e8	+	5.65503e7i	0.334201	+	0.168215i
$274$	9.45813e7	+	1.22822e8i	0.277765	+	0.360702i
$275$	−2.24602e8	+	1.29674e8i	−0.651252	+	0.376000i
$276$	−3.16519e8	+	3.57506e8i	−0.906187	+	1.02353i
$277$	7.03836e7	+	4.06360e7i	0.198972	+	0.114877i	0.596176	−	0.802854i	$-0.296686\pi$
$277$	7.03836e7	+	4.06360e7i	0.198972	+	0.114877i	−0.397204	+	0.917730i	$0.630019\pi$
$278$	1.54092e7	+	1.15506e8i	0.0430154	+	0.322438i
$279$	−2.51831e8	−	1.09162e8i	−0.694216	−	0.300924i
$280$	5.77404e8	−	2.42675e8i	1.57191	−	0.660650i
$281$	−2.78466e8	−	1.60773e8i	−0.748687	−	0.432255i	0.0765320	−	0.997067i	$-0.475615\pi$
$281$	−2.78466e8	−	1.60773e8i	−0.748687	−	0.432255i	−0.825219	+	0.564812i	$0.808949\pi$
$282$	5.46726e8	−	1.05095e8i	1.45177	−	0.279069i
$283$	7.45125e7	+	1.29059e8i	0.195423	+	0.338483i	0.947039	−	0.321118i	$-0.104059\pi$
$283$	7.45125e7	+	1.29059e8i	0.195423	+	0.338483i	−0.751616	+	0.659601i	$0.770725\pi$
$284$	3.77361e8	+	3.74768e8i	0.977558	+	0.970840i
$285$	3.26774e7	+	5.69796e8i	0.0836162	+	1.45802i
$286$	9.03742e7	+	3.72518e7i	0.228435	+	0.0941600i
$287$	−2.71164e8			−0.677088
$288$	3.92374e8	−	1.01902e8i	0.967892	−	0.251367i
$289$	4.09280e8			0.997420
$290$	−2.40912e8	−	9.93028e7i	−0.580050	−	0.239094i
$291$	−2.67864e8	+	1.75835e8i	−0.637219	+	0.418293i
$292$	−4.33358e8	−	4.30380e8i	−1.01861	−	1.01161i
$293$	−1.93693e6	−	3.35487e6i	−0.00449861	−	0.00779182i	0.863767	−	0.503891i	$-0.168099\pi$
$293$	−1.93693e6	−	3.35487e6i	−0.00449861	−	0.00779182i	−0.868266	+	0.496099i	$0.834765\pi$
$294$	7.25938e7	−	2.09414e8i	0.166603	−	0.480607i
$295$	2.24116e7	+	1.29393e7i	0.0508271	+	0.0293450i
$296$	−6.16278e7	+	2.59013e7i	−0.138120	+	0.0580497i
$297$	−1.26173e8	+	3.43796e8i	−0.279460	+	0.761470i
$298$	−7.53824e7	−	5.65057e8i	−0.165011	−	1.23690i
$299$	−1.66689e8	−	9.62381e7i	−0.360627	−	0.208208i
$300$	−4.24828e8	−	8.65881e7i	−0.908424	−	0.185154i
$301$	8.76920e8	−	5.06290e8i	1.85343	−	1.07008i
$302$	−3.33057e8	−	4.32503e8i	−0.695816	−	0.903576i
$303$	3.16528e8	−	2.07780e8i	0.653677	−	0.429096i
$304$	−3.55327e6	−	5.15312e8i	−0.00725389	−	1.05199i
$305$		−	1.21018e9i		−	2.44232i
$306$	−2.46829e7	+	6.22892e6i	−0.0492460	+	0.0124276i
$307$	−2.85809e8			−0.563756			−0.281878	−	0.959450i	$-0.590957\pi$
$307$	−2.85809e8			−0.563756			−0.281878	+	0.959450i	$0.590957\pi$
$308$	1.30522e8	−	4.93921e8i	0.254541	−	0.963230i
$309$	−4.45498e8	+	2.55490e7i	−0.858995	+	0.0492628i
$310$	−3.36143e8	−	4.36510e8i	−0.640852	−	0.832200i
$311$	2.76466e8	+	4.78853e8i	0.521171	+	0.902694i	0.999697	+	0.0246207i	$0.00783781\pi$
$311$	2.76466e8	+	4.78853e8i	0.521171	+	0.902694i	−0.478526	+	0.878073i	$0.658829\pi$
$312$	7.18372e7	+	1.46777e8i	0.133909	+	0.273600i
$313$	9.43439e7	−	1.63408e8i	0.173904	−	0.301210i	−0.765878	−	0.642986i	$-0.777695\pi$
$313$	9.43439e7	−	1.63408e8i	0.173904	−	0.301210i	0.939781	+	0.341776i	$0.111029\pi$
$314$	5.28930e8	−	7.05627e7i	0.964150	−	0.128624i
$315$	−7.59717e8	+	5.63487e8i	−1.36951	+	1.01577i
$316$	−1.49892e8	−	5.51789e8i	−0.267224	−	0.983713i
$317$	3.80535e8	−	6.59105e8i	0.670945	−	1.16211i	−0.306692	−	0.951809i	$-0.599222\pi$
$317$	3.80535e8	−	6.59105e8i	0.670945	−	1.16211i	0.977637	−	0.210301i	$-0.0674445\pi$
$318$	6.81303e8	+	7.87044e8i	1.18808	+	1.37247i
$319$	−1.84068e8	+	1.06272e8i	−0.317476	+	0.183295i
$320$	7.88133e8	+	2.02467e8i	1.34454	+	0.345405i
$321$	4.47788e8	−	8.89641e8i	0.755622	−	1.50123i
$322$	−3.83354e8	+	9.30030e8i	−0.639889	+	1.55239i
$323$			3.23601e7i			0.0534319i
$324$	−5.38911e8	+	2.90497e8i	−0.880257	+	0.474498i
$325$		−	1.74770e8i		−	0.282406i
$326$	−1.02202e9	−	4.21272e8i	−1.63380	−	0.673443i
$327$	4.48713e8	−	8.91480e8i	0.709662	−	1.40992i
$328$	−2.80600e8	−	2.13016e8i	−0.439066	−	0.333314i
$329$	1.01576e9	−	5.86448e8i	1.57255	−	0.907911i
$330$	−5.55782e8	+	4.81112e8i	−0.851345	+	0.736965i
$331$	1.59263e8	−	2.75851e8i	0.241388	−	0.418096i	−0.719722	−	0.694263i	$-0.755731\pi$
$331$	1.59263e8	−	2.75851e8i	0.241388	−	0.418096i	0.961110	+	0.276166i	$0.0890640\pi$
$332$	2.26396e8	+	8.33417e8i	0.339536	+	1.24991i
$333$	8.10864e7	−	6.01423e7i	0.120335	−	0.0892535i
$334$	1.18850e8	+	8.90885e8i	0.174537	+	1.30831i
$335$	−2.57916e8	+	4.46723e8i	−0.374819	+	0.649205i
$336$	7.10719e8	−	4.73585e8i	1.02214	−	0.681099i
$337$	−4.96417e8	−	8.59820e8i	−0.706549	−	1.22378i	−0.966130	−	0.258058i	$-0.916918\pi$
$337$	−4.96417e8	−	8.59820e8i	−0.706549	−	1.22378i	0.259580	−	0.965721i	$-0.416416\pi$
$338$	5.10279e8	−	3.92951e8i	0.718786	−	0.553515i
$339$	−3.11431e8	+	1.78604e7i	−0.434173	+	0.0248995i
$340$	−4.94024e7	−	1.30550e7i	−0.0681667	−	0.0180135i
$341$	−4.49382e8			−0.613728
$342$	1.90425e8	+	7.54584e8i	0.257415	+	1.02004i
$343$			4.51028e8i			0.603495i
$344$	1.30516e9	+	1.64965e8i	1.72866	+	0.218493i
$345$	1.21002e9	−	7.94302e8i	1.58645	−	1.04140i
$346$	8.03319e6	−	6.18612e6i	0.0104261	−	0.00802882i
$347$	−1.11618e8	+	6.44426e7i	−0.143410	+	0.0827981i	−0.569988	−	0.821653i	$-0.693052\pi$
$347$	−1.11618e8	+	6.44426e7i	−0.143410	+	0.0827981i	0.426578	+	0.904451i	$0.359719\pi$
$348$	−3.48159e8	−	7.09615e7i	−0.442843	−	0.0902600i
$349$	−2.42119e8	−	1.39788e8i	−0.304888	−	0.176027i	0.339749	−	0.940516i	$-0.389658\pi$
$349$	−2.42119e8	−	1.39788e8i	−0.304888	−	0.176027i	−0.644637	+	0.764489i	$0.722991\pi$
$350$	−9.05380e8	+	1.20784e8i	−1.12874	+	0.150581i
$351$	−1.58126e8	−	1.89473e8i	−0.195177	−	0.233869i
$352$	5.23069e8	−	4.08576e8i	0.639234	−	0.499314i
$353$	−7.63646e6	−	4.40891e6i	−0.00924018	−	0.00533482i	0.495373	−	0.868680i	$-0.335031\pi$
$353$	−7.63646e6	−	4.40891e6i	−0.00924018	−	0.00533482i	−0.504613	+	0.863346i	$0.668365\pi$
$354$	3.33413e7	+	1.15578e7i	0.0399458	+	0.0138473i
$355$	−8.06096e8	−	1.39620e9i	−0.956285	−	1.65633i
$356$	−2.48007e8	+	2.49723e8i	−0.291332	+	0.293348i
$357$	−4.48340e7	+	2.94306e7i	−0.0521517	+	0.0342342i
$358$	−6.39964e8	+	1.55257e9i	−0.737166	+	1.78839i
$359$	4.37080e8			0.498575			0.249288	−	0.968429i	$-0.419804\pi$
$359$	4.37080e8			0.498575			0.249288	+	0.968429i	$0.419804\pi$
$360$	−1.22881e9	−	1.37081e7i	−1.38811	−	0.0154852i
$361$	9.54121e7			0.106740
$362$	−1.14087e8	+	2.76778e8i	−0.126402	+	0.306656i
$363$	−1.78483e7	−	3.11222e8i	−0.0195851	−	0.341505i
$364$	2.44273e8	+	2.42595e8i	0.265473	+	0.263649i
$365$	9.25713e8	+	1.60338e9i	0.996441	+	1.72589i
$366$	−3.11507e8	−	1.62052e9i	−0.332112	−	1.72771i
$367$	−1.51115e8	−	8.72464e7i	−0.159579	−	0.0921333i	0.418084	−	0.908409i	$-0.362702\pi$
$367$	−1.51115e8	−	8.72464e7i	−0.159579	−	0.0921333i	−0.577663	+	0.816275i	$0.696035\pi$
$368$	−1.12729e9	+	6.61247e8i	−1.17915	+	0.691666i
$369$	4.88148e8	+	2.11599e8i	0.505777	+	0.219241i
$370$	2.00865e8	−	2.67968e7i	0.206157	−	0.0275028i
$371$	1.89923e9	+	1.09652e9i	1.93094	+	1.11483i
$372$	−5.62478e8	−	4.97992e8i	−0.566507	−	0.501559i
$373$	−3.75268e8	+	2.16661e8i	−0.374422	+	0.216172i	−0.675388	−	0.737462i	$-0.736024\pi$
$373$	−3.75268e8	+	2.16661e8i	−0.374422	+	0.216172i	0.300967	+	0.953635i	$0.402691\pi$
$374$	−3.30225e7	+	2.54297e7i	−0.0326407	+	0.0251356i
$375$	−9.23096e7	−	4.64627e7i	−0.0903936	−	0.0454983i
$376$	1.51179e9	+	1.91083e8i	1.46668	+	0.185381i
$377$		−	1.43229e8i		−	0.137669i
$378$	−8.72269e8	+	9.50102e8i	−0.830672	+	0.904793i
$379$	8.33881e8			0.786804			0.393402	−	0.919366i	$-0.371298\pi$
$379$	8.33881e8			0.786804			0.393402	+	0.919366i	$0.371298\pi$
$380$	−3.99105e8	+	1.51029e9i	−0.373117	+	1.41194i
$381$	−2.90466e8	+	5.77082e8i	−0.269065	+	0.534565i
$382$	1.06526e9	−	8.20326e8i	0.977766	−	0.752947i
$383$	−2.42102e8	−	4.19333e8i	−0.220192	−	0.381385i	0.734674	−	0.678420i	$-0.237335\pi$
$383$	−2.42102e8	−	4.19333e8i	−0.220192	−	0.381385i	−0.954866	+	0.297036i	$0.904002\pi$
$384$	1.10748e9	+	6.82477e7i	0.998107	+	0.0615076i
$385$	−7.74324e8	+	1.34117e9i	−0.691528	+	1.19776i
$386$	−1.14188e7	−	8.55941e7i	−0.0101057	−	0.0757510i
$387$	−1.97370e9	+	2.27128e8i	−1.73099	+	0.199197i
$388$	−8.46341e8	+	2.29907e8i	−0.735588	+	0.199821i
$389$	1.26226e8	−	2.18631e8i	0.108724	−	0.188316i	−0.806529	−	0.591194i	$-0.798657\pi$
$389$	1.26226e8	−	2.18631e8i	0.108724	−	0.188316i	0.915254	+	0.402878i	$0.131990\pi$
$390$	−9.35104e7	−	4.86459e8i	−0.0798241	−	0.415260i
$391$	7.10734e7	−	4.10343e7i	0.0601296	−	0.0347159i
$392$	3.66807e8	−	4.83186e8i	0.307565	−	0.405147i
$393$	1.33553e9	−	7.65918e7i	1.10989	−	0.0636515i
$394$	−6.14742e8	−	2.53394e8i	−0.506356	−	0.208718i
$395$			1.73329e9i			1.41508i
$396$	−6.20390e8	+	7.87302e8i	−0.502032	+	0.637101i
$397$			5.05463e8i			0.405436i	0.979237	+	0.202718i	$0.0649775\pi$
$397$			5.05463e8i			0.405436i	−0.979237	+	0.202718i	$0.935023\pi$
$398$	3.04244e8	−	7.38105e8i	0.241897	−	0.586851i
$399$	8.99726e8	+	1.37063e9i	0.709096	+	1.08022i
$400$	−1.03177e9	−	5.86244e8i	−0.806070	−	0.458003i
$401$	−1.44360e8	+	8.33464e7i	−0.111800	+	0.0645478i	−0.554857	−	0.831945i	$-0.687227\pi$
$401$	−1.44360e8	+	8.33464e7i	−0.111800	+	0.0645478i	0.443057	+	0.896493i	$0.353894\pi$
$402$	−2.30378e8	+	6.64582e8i	−0.176869	+	0.510220i
$403$	1.51415e8	−	2.62259e8i	0.115240	−	0.199601i
$404$	1.00010e9	−	2.71675e8i	0.754586	−	0.204982i
$405$	1.80735e9	−	4.21551e8i	1.35191	−	0.315324i
$406$	−7.41986e8	+	9.89858e7i	−0.550243	+	0.0734060i
$407$	8.26454e7	−	1.43146e8i	0.0607629	−	0.105244i
$408$	−6.95137e7	−	4.76507e6i	−0.0506710	−	0.00347343i
$409$	−7.47564e7	−	1.29482e8i	−0.0540277	−	0.0935787i	0.837747	−	0.546059i	$-0.183873\pi$
$409$	−7.47564e7	−	1.29482e8i	−0.0540277	−	0.0935787i	−0.891774	+	0.452480i	$0.850539\pi$
$410$	6.51576e8	+	8.46127e8i	0.466898	+	0.606306i
$411$	−3.51633e8	−	5.35671e8i	−0.249829	−	0.380585i
$412$	−1.18083e9	−	3.12042e8i	−0.831852	−	0.219823i
$413$	7.43419e7			0.0519288
$414$	1.41585e9	−	1.37509e9i	0.980654	−	0.952423i
$415$		−	2.61794e9i		−	1.79801i
$416$	6.22009e7	+	4.42928e8i	0.0423614	+	0.301652i
$417$	−2.75784e7	−	4.80884e8i	−0.0186248	−	0.324761i
$418$	7.77414e8	+	1.00954e9i	0.520637	+	0.676091i
$419$	1.00822e9	−	5.82093e8i	0.669583	−	0.386584i	−0.126336	−	0.991988i	$-0.540322\pi$
$419$	1.00822e9	−	5.82093e8i	0.669583	−	0.386584i	0.795918	+	0.605404i	$0.206988\pi$
$420$	−2.45544e9	+	8.20616e8i	−1.61717	+	0.540465i
$421$	−1.48673e9	−	8.58366e8i	−0.971059	−	0.560641i	−0.0715001	−	0.997441i	$-0.522779\pi$
$421$	−1.48673e9	−	8.58366e8i	−0.971059	−	0.560641i	−0.899559	+	0.436799i	$0.856112\pi$
$422$	−9.97999e7	−	7.48089e8i	−0.0646453	−	0.484573i
$423$	−2.28619e9	+	2.63088e8i	−1.46866	+	0.169009i
$424$	1.10394e9	+	2.62664e9i	0.703339	+	1.67348i
$425$	6.45352e7	+	3.72594e7i	0.0407789	+	0.0235437i
$426$	−1.43881e9	−	1.66211e9i	−0.901714	−	1.04166i
$427$	−1.73826e9	−	3.01075e9i	−1.08048	−	1.87144i
$428$	1.92096e9	−	1.93425e9i	1.18431	−	1.19250i
$429$	−3.60914e8	−	1.81661e8i	−0.220700	−	0.111086i
$430$	−3.68694e9	−	1.51974e9i	−2.23628	−	0.921786i
$431$	−3.99728e8			−0.240488			−0.120244	−	0.992744i	$-0.538368\pi$
$431$	−3.99728e8			−0.240488			−0.120244	+	0.992744i	$0.538368\pi$
$432$	−1.64899e9	+	2.97945e8i	−0.984066	+	0.177805i
$433$	−2.33544e9			−1.38248			−0.691242	−	0.722623i	$-0.742936\pi$
$433$	−2.33544e9			−1.38248			−0.691242	+	0.722623i	$0.742936\pi$
$434$	−1.46325e9	−	6.03146e8i	−0.859222	−	0.354167i
$435$	9.62094e8	+	4.84256e8i	0.560409	+	0.282074i
$436$	1.92493e9	−	1.93825e9i	1.11228	−	1.11997i
$437$	−1.25446e9	−	2.17280e9i	−0.719074	−	1.24547i
$438$	1.65231e9	+	1.90876e9i	0.939578	+	1.08540i
$439$	1.06189e9	+	6.13081e8i	0.599036	+	0.345853i	0.768662	−	0.639655i	$-0.220923\pi$
$439$	1.06189e9	+	6.13081e8i	0.599036	+	0.345853i	−0.169626	+	0.985508i	$0.554256\pi$
$440$	−1.85484e9	+	7.79561e8i	−1.03806	+	0.436281i
$441$	−3.64367e8	+	8.40577e8i	−0.202304	+	0.466705i
$442$	−3.71407e6	−	2.78402e7i	−0.00204584	−	0.0153354i
$443$	2.76520e9	+	1.59649e9i	1.51117	+	0.872476i	0.999915	+	0.0130486i	$0.00415363\pi$
$443$	2.76520e9	+	1.59649e9i	1.51117	+	0.872476i	0.511258	+	0.859427i	$0.329180\pi$
$444$	2.62075e8	−	8.75864e7i	0.142097	−	0.0474893i
$445$	9.23951e8	−	5.33443e8i	0.497037	−	0.286964i
$446$	1.79846e9	+	2.33545e9i	0.959905	+	1.24652i
$447$	1.34914e8	+	2.35250e9i	0.0714466	+	1.24581i
$448$	2.25157e9	−	6.28335e8i	1.18307	−	0.330155i
$449$		−	4.54934e8i		−	0.237185i	−0.992943	−	0.118592i	$-0.962162\pi$
$449$		−	4.54934e8i		−	0.237185i	0.992943	−	0.118592i	$-0.0378382\pi$
$450$	1.72411e9	+	4.89067e8i	0.891912	+	0.253002i
$451$	8.71079e8			0.447136
$452$	−8.25473e8	−	2.18137e8i	−0.420454	−	0.111108i
$453$	1.23823e9	+	1.88630e9i	0.625834	+	0.953384i
$454$	8.70452e8	+	1.13036e9i	0.436565	+	0.566917i
$455$	−5.21802e8	−	9.03788e8i	−0.259697	−	0.449808i
$456$	−1.45674e8	+	2.12511e9i	−0.0719456	+	1.04955i
$457$	−1.78198e9	+	3.08649e9i	−0.873368	+	1.51272i	−0.0148764	+	0.999889i	$0.504735\pi$
$457$	−1.78198e9	+	3.08649e9i	−0.873368	+	1.51272i	−0.858491	+	0.512828i	$0.828598\pi$
$458$	3.05123e9	−	4.07054e8i	1.48404	−	0.197981i
$459$	1.03676e8	−	1.79952e7i	0.0500417	−	0.00868584i
$460$	3.82318e9	−	1.03856e9i	1.83136	−	0.497484i
$461$	−1.58069e9	+	2.73783e9i	−0.751438	+	1.30153i	0.195688	+	0.980666i	$0.437306\pi$
$461$	−1.58069e9	+	2.73783e9i	−0.751438	+	1.30153i	−0.947126	+	0.320863i	$0.896027\pi$
$462$	−6.91650e8	+	1.99523e9i	−0.326317	+	0.941339i
$463$	2.83365e9	−	1.63601e9i	1.32682	−	0.766041i	0.342015	−	0.939695i	$-0.388891\pi$
$463$	2.83365e9	−	1.63601e9i	1.32682	−	0.766041i	0.984807	+	0.173654i	$0.0555575\pi$
$464$	−8.45566e8	−	4.80444e8i	−0.392947	−	0.223270i
$465$	1.24971e9	+	1.90378e9i	0.576398	+	0.878074i
$466$	−6.68787e8	+	1.62250e9i	−0.306152	+	0.742735i
$467$			6.91876e8i			0.314354i	0.987570	+	0.157177i	$0.0502393\pi$
$467$			6.91876e8i			0.314354i	−0.987570	+	0.157177i	$0.949761\pi$
$468$	−2.50434e8	−	6.27333e8i	−0.112936	−	0.282903i
$469$			1.48184e9i			0.663278i
$470$	−4.27067e9	−	1.76035e9i	−1.89738	−	0.782091i
$471$	−2.20209e9	+	1.26288e8i	−0.971096	+	0.0556917i
$472$	7.69290e7	+	5.84001e7i	0.0336739	+	0.0255633i
$473$	−2.81699e9	+	1.62639e9i	−1.22397	+	0.706661i
$474$	4.46157e8	+	2.32099e9i	0.192426	+	1.00104i
$475$	1.13906e9	−	1.97291e9i	0.487663	−	0.844657i
$476$	−1.41657e8	+	3.84808e7i	−0.0602024	+	0.0163538i
$477$	−2.56333e9	−	3.45599e9i	−1.08141	−	1.45800i
$478$	4.67835e8	+	3.50684e9i	0.195927	+	1.46865i
$479$	−7.80578e8	+	1.35200e9i	−0.324520	+	0.562086i	−0.981415	−	0.191897i	$-0.938536\pi$
$479$	−7.80578e8	+	1.35200e9i	−0.324520	+	0.562086i	0.656895	+	0.753982i	$0.271870\pi$
$480$	−3.18553e9	−	1.07972e9i	−1.31473	−	0.445623i
$481$	5.56932e7	+	9.64635e7i	0.0228189	+	0.0395235i
$482$	2.92825e9	−	2.25496e9i	1.19109	−	0.917220i
$483$	1.86945e9	−	3.71412e9i	0.754916	−	1.49983i
$484$	2.17991e8	−	8.24918e8i	0.0873935	−	0.330713i
$485$	2.65854e9			1.05815
$486$	2.31165e9	−	1.02971e9i	0.913473	−	0.406899i
$487$			1.16011e9i			0.455145i	0.973761	+	0.227572i	$0.0730788\pi$
$487$			1.16011e9i			0.455145i	−0.973761	+	0.227572i	$0.926921\pi$
$488$	5.66379e8	−	4.48103e9i	0.220616	−	1.74545i
$489$	4.08149e9	+	2.05436e9i	1.57847	+	0.794502i
$490$	−1.45701e9	+	1.12200e9i	−0.559468	+	0.430829i
$491$	−2.30773e9	+	1.33237e9i	−0.879833	+	0.507972i	−0.870603	−	0.491985i	$-0.836271\pi$
$491$	−2.30773e9	+	1.33237e9i	−0.879833	+	0.507972i	−0.00922981	+	0.999957i	$0.502938\pi$
$492$	1.09030e9	+	9.65304e8i	0.412733	+	0.365415i
$493$	5.28885e7	+	3.05352e7i	0.0198791	+	0.0114772i
$494$	−8.51107e8	+	1.13543e8i	−0.317643	+	0.0423757i
$495$	2.44049e9	−	1.81013e9i	0.904398	−	0.670798i
$496$	−1.04037e9	−	1.77361e9i	−0.382825	−	0.652638i
$497$	−4.01088e9	−	2.31568e9i	−1.46552	−	0.846120i
$498$	−6.73870e8	−	3.50560e9i	−0.244497	−	1.27192i
$499$	−1.20231e9	−	2.08246e9i	−0.433176	−	0.750283i	0.563969	−	0.825796i	$-0.309274\pi$
$499$	−1.20231e9	−	2.08246e9i	−0.433176	−	0.750283i	−0.997145	+	0.0755129i	$0.975941\pi$
$500$	−2.00699e8	−	1.99320e8i	−0.0718043	−	0.0713109i
$501$	−2.12710e8	−	3.70902e9i	−0.0755710	−	1.31773i
$502$	1.30537e9	−	3.16687e9i	0.460543	−	1.11729i
$503$	−7.95547e8			−0.278726			−0.139363	−	0.990241i	$-0.544506\pi$
$503$	−7.95547e8			−0.278726			−0.139363	+	0.990241i	$0.544506\pi$
$504$	−3.07677e9	+	1.73090e9i	−1.07050	+	0.602235i
$505$	−3.14153e9			−1.08548
$506$	1.23148e9	−	2.98761e9i	0.422571	−	1.02517i
$507$	−2.22552e9	+	1.46091e9i	−0.758408	+	0.497845i
$508$	−1.24607e9	+	1.25469e9i	−0.421715	+	0.424632i
$509$	−5.20410e8	−	9.01377e8i	−0.174918	−	0.302966i	0.765215	−	0.643775i	$-0.222633\pi$
$509$	−5.20410e8	−	9.01377e8i	−0.174918	−	0.302966i	−0.940133	+	0.340809i	$0.889299\pi$
$510$	1.99565e8	+	6.91795e7i	0.0666175	+	0.0230931i
$511$	4.60606e9	+	2.65931e9i	1.52706	+	0.881649i
$512$	2.82352e9	+	1.11854e9i	0.929705	+	0.368305i
$513$	−5.50133e8	−	3.16948e9i	−0.179911	−	1.03652i
$514$	4.26107e9	−	5.68455e8i	1.38404	−	0.184640i
$515$	3.20636e9	+	1.85119e9i	1.03440	+	0.597208i
$516$	−5.32826e9	−	1.08600e9i	−1.70731	−	0.347982i
$517$	−3.26299e9	+	1.88389e9i	−1.03848	+	0.599568i
$518$	4.61232e8	−	3.55180e8i	0.145802	−	0.112278i
$519$	−3.50357e7	+	2.29986e7i	−0.0110008	+	0.00722132i
$520$	1.70020e8	−	1.34515e9i	0.0530259	−	0.419525i
$521$			8.86513e8i			0.274633i	0.990527	+	0.137317i	$0.0438478\pi$
$521$			8.86513e8i			0.274633i	−0.990527	+	0.137317i	$0.956152\pi$
$522$	1.41296e9	+	4.00805e8i	0.434794	+	0.123335i
$523$	1.91552e9			0.585506			0.292753	−	0.956188i	$-0.405429\pi$
$523$	1.91552e9			0.585506			0.292753	+	0.956188i	$0.405429\pi$
$524$	3.53993e9	+	9.35454e8i	1.07482	+	0.284029i
$525$	3.76936e9	−	2.16170e8i	1.13687	−	0.0651987i
$526$	9.50960e7	−	7.32305e7i	0.0284913	−	0.0219403i
$527$	6.45608e7	+	1.11823e8i	0.0192146	+	0.0332807i
$528$	−2.28309e9	+	1.52133e9i	−0.675002	+	0.449785i
$529$	−1.47904e9	+	2.56178e9i	−0.434396	+	0.752396i
$530$	−1.14211e9	−	8.56109e9i	−0.333227	−	2.49783i
$531$	−1.33830e8	−	5.80117e7i	−0.0387902	−	0.0168145i
$532$	1.17640e9	+	4.33062e9i	0.338739	+	1.24698i
$533$	−2.93502e8	+	5.08361e8i	−0.0839588	+	0.145421i
$534$	1.09992e9	−	9.52146e8i	0.312585	−	0.270588i
$535$	−7.15656e9	+	4.13184e9i	−2.02053	+	1.16655i
$536$	−1.16407e9	+	1.53340e9i	−0.326515	+	0.430110i
$537$	3.12082e9	−	6.20029e9i	0.869679	−	1.72783i
$538$	2.65410e9	+	1.09401e9i	0.734819	+	0.302889i
$539$			1.49997e9i			0.412594i
$540$	5.06062e9	+	4.38798e8i	1.38301	+	0.119919i
$541$		−	5.95706e9i		−	1.61749i	−0.588159	−	0.808745i	$-0.700147\pi$
$541$		−	5.95706e9i		−	1.61749i	0.588159	−	0.808745i	$-0.299853\pi$
$542$	1.32548e9	−	3.21565e9i	0.357581	−	0.867504i
$543$	5.56351e8	−	1.10533e9i	0.149125	−	0.296273i
$544$	−1.76816e8	−	7.14603e7i	−0.0470895	−	0.0190313i
$545$	−7.17135e9	+	4.14038e9i	−1.89764	+	1.09560i
$546$	−9.31369e8	−	1.07592e9i	−0.244877	−	0.282882i
$547$	1.20704e9	−	2.09066e9i	0.315331	−	0.546170i	−0.664177	−	0.747576i	$-0.731218\pi$
$547$	1.20704e9	−	2.09066e9i	0.315331	−	0.546170i	0.979508	+	0.201406i	$0.0645511\pi$
$548$	−4.59764e8	−	1.69250e9i	−0.119345	−	0.439336i
$549$	7.79804e8	+	6.77636e9i	0.201132	+	1.74781i
$550$	2.90842e9	−	3.88002e8i	0.745397	−	0.0994409i
$551$	9.33495e8	−	1.61686e9i	0.237729	−	0.411758i
$552$	4.85217e9	−	2.37481e9i	1.22786	−	0.600954i
$553$	2.48962e9	+	4.31215e9i	0.626030	+	1.08432i
$554$	−5.61005e8	−	7.28512e8i	−0.140179	−	0.182034i
$555$	−8.36261e8	+	4.79590e7i	−0.207643	+	0.0119082i
$556$	3.36828e8	−	1.27462e9i	0.0831087	−	0.314499i
$557$	3.06131e9			0.750609			0.375305	−	0.926902i	$-0.377538\pi$
$557$	3.06131e9			0.750609			0.375305	+	0.926902i	$0.377538\pi$
$558$	2.16348e9	+	2.22761e9i	0.527150	+	0.542775i
$559$		−	2.19199e9i		−	0.530759i
$560$	−7.08592e9	+	4.88602e7i	−1.70505	+	0.0117570i
$561$	1.44023e8	−	9.45420e7i	0.0344400	−	0.0226076i
$562$	2.21957e9	+	2.88229e9i	0.527462	+	0.684954i
$563$	−5.63372e9	+	3.25263e9i	−1.33050	+	0.768166i	−0.985377	−	0.170390i	$-0.945497\pi$
$563$	−5.63372e9	+	3.25263e9i	−1.33050	+	0.768166i	−0.345126	+	0.938556i	$0.612164\pi$
$564$	−6.17185e9	−	1.25794e9i	−1.44857	−	0.295246i
$565$	2.24145e9	+	1.29410e9i	0.522828	+	0.301855i
$566$	−2.22952e8	−	1.67122e9i	−0.0516836	−	0.387414i
$567$	3.89090e9	−	3.64475e9i	0.896415	−	0.839705i
$568$	−2.33135e9	−	5.54706e9i	−0.533811	−	1.27012i
$569$	3.23442e9	+	1.86739e9i	0.736044	+	0.424955i	0.820629	−	0.571461i	$-0.193623\pi$
$569$	3.23442e9	+	1.86739e9i	0.736044	+	0.424955i	−0.0845851	+	0.996416i	$0.526956\pi$
$570$	2.11490e9	−	6.10092e9i	0.478329	−	1.37986i
$571$	1.87755e9	+	3.25202e9i	0.422052	+	0.731015i	0.996140	−	0.0877785i	$-0.0279768\pi$
$571$	1.87755e9	+	3.25202e9i	0.422052	+	0.731015i	−0.574088	+	0.818793i	$0.694643\pi$
$572$	−7.84697e8	−	7.79305e8i	−0.175314	−	0.174109i
$573$	−4.64600e9	+	3.04979e9i	−1.03166	+	0.677219i
$574$	2.83636e9	+	1.16913e9i	0.625993	+	0.258032i
$575$	−5.77757e9			−1.26738
$576$	−4.54357e9	−	6.25853e8i	−0.990646	−	0.136456i
$577$	−5.28968e9			−1.14634			−0.573171	−	0.819436i	$-0.694287\pi$
$577$	−5.28968e9			−1.14634			−0.573171	+	0.819436i	$0.694287\pi$
$578$	−4.28105e9	−	1.76463e9i	−0.922153	−	0.380107i
$579$	2.04366e7	+	3.56353e8i	0.00437556	+	0.0762967i
$580$	2.09178e9	+	2.07741e9i	0.445162	+	0.442103i
$581$	−3.76030e9	−	6.51303e9i	−0.795437	−	1.37774i
$582$	3.55997e9	−	6.84320e8i	0.748541	−	0.143889i
$583$	−6.10104e9	−	3.52244e9i	−1.27516	−	0.736212i
$584$	2.67730e9	+	6.37019e9i	0.556227	+	1.32345i
$585$	2.34087e8	+	2.03418e9i	0.0483428	+	0.420091i
$586$	5.79557e6	+	4.34429e7i	0.00118975	+	0.00891820i
$587$	6.97118e9	+	4.02481e9i	1.42257	+	0.821320i	0.996518	−	0.0833796i	$-0.0265714\pi$
$587$	6.97118e9	+	4.02481e9i	1.42257	+	0.821320i	0.426050	+	0.904700i	$0.359905\pi$
$588$	−1.66223e9	+	1.87747e9i	−0.337186	+	0.380849i
$589$	3.41855e9	−	1.97370e9i	0.689347	−	0.397995i
$590$	−1.78635e8	−	2.31973e8i	−0.0358084	−	0.0465003i
$591$	2.45500e9	+	1.23569e9i	0.489210	+	0.246237i
$592$	7.56298e8	−	5.21496e6i	0.149819	−	0.00103306i
$593$		−	7.53009e9i		−	1.48289i	−0.671014	−	0.741444i	$-0.734141\pi$
$593$		−	7.53009e9i		−	1.48289i	0.671014	−	0.741444i	$-0.265859\pi$
$594$	2.80206e9	−	3.05208e9i	0.548560	−	0.597508i
$595$	4.44975e8			0.0866017
$596$	−1.64777e9	+	6.23549e9i	−0.318813	+	1.20645i
$597$	−1.48366e9	+	2.94766e9i	−0.285381	+	0.566980i
$598$	1.32863e9	+	1.72533e9i	0.254067	+	0.329928i
$599$	1.06989e9	+	1.85311e9i	0.203398	+	0.352295i	0.949621	−	0.313400i	$-0.101468\pi$
$599$	1.06989e9	+	1.85311e9i	0.203398	+	0.352295i	−0.746223	+	0.665696i	$0.768135\pi$
$600$	4.07035e9	+	2.73737e9i	0.769312	+	0.517374i
$601$	−5.22338e7	+	9.04716e7i	−0.00981502	+	0.0170001i	−0.870891	−	0.491476i	$-0.836458\pi$
$601$	−5.22338e7	+	9.04716e7i	−0.00981502	+	0.0170001i	0.861076	+	0.508476i	$0.169791\pi$
$602$	−1.13554e10	+	1.51489e9i	−2.12137	+	0.283004i
$603$	1.15633e9	−	2.66759e9i	0.214769	−	0.495461i
$604$	1.61901e9	+	5.95995e9i	0.298964	+	1.10056i
$605$	−1.29323e9	+	2.23994e9i	−0.237428	+	0.411237i
$606$	−4.20672e9	+	8.08644e8i	−0.767874	+	0.147606i
$607$	3.95742e9	−	2.28482e9i	0.718210	−	0.414659i	−0.0958833	−	0.995393i	$-0.530568\pi$
$607$	3.95742e9	−	2.28482e9i	0.718210	−	0.414659i	0.814094	+	0.580734i	$0.197234\pi$
$608$	−2.18462e9	+	5.40546e9i	−0.394197	+	0.975371i
$609$	3.08910e9	−	1.77158e8i	0.554207	−	0.0317834i
$610$	−5.21776e9	+	1.26585e10i	−0.930743	+	2.25801i
$611$		−	2.53904e9i		−	0.450323i
$612$	2.85038e8	+	4.12672e7i	0.0502659	+	0.00727737i
$613$		−	1.42590e9i		−	0.250021i	−0.992155	−	0.125010i	$-0.960104\pi$
$613$		−	1.42590e9i		−	0.250021i	0.992155	−	0.125010i	$-0.0398964\pi$
$614$	2.98954e9	+	1.23228e9i	0.521213	+	0.214842i
$615$	−2.42242e9	−	3.69027e9i	−0.419939	−	0.639728i
$616$	−3.49482e9	+	4.60364e9i	−0.602410	+	0.793539i
$617$	−3.18239e9	+	1.83735e9i	−0.545450	+	0.314916i	−0.747285	−	0.664504i	$-0.768643\pi$
$617$	−3.18239e9	+	1.83735e9i	−0.545450	+	0.314916i	0.201835	+	0.979420i	$0.435310\pi$
$618$	4.77004e9	+	1.65354e9i	0.812947	+	0.281809i
$619$	2.60174e8	−	4.50635e8i	0.0440907	−	0.0763674i	−0.843138	−	0.537697i	$-0.819294\pi$
$619$	2.60174e8	−	4.50635e8i	0.0440907	−	0.0763674i	0.887229	+	0.461330i	$0.152628\pi$
$620$	1.63401e9	+	6.01516e9i	0.275348	+	1.01362i
$621$	−6.26364e9	+	5.22735e9i	−1.04956	+	0.875912i
$622$	−8.27224e8	−	6.20077e9i	−0.137834	−	1.03319i
$623$	1.53243e9	−	2.65425e9i	0.253906	−	0.439777i
$624$	−1.18579e8	−	1.84501e9i	−0.0195372	−	0.303985i
$625$	3.25801e9	+	5.64304e9i	0.533792	+	0.924555i
$626$	−1.69137e9	+	1.30248e9i	−0.275569	+	0.212207i
$627$	−2.89026e9	−	4.40296e9i	−0.468274	−	0.713360i
$628$	−5.83682e9	−	1.54242e9i	−0.940410	−	0.248510i
$629$	−4.74933e7			−0.00760948
$630$	1.03761e10	−	2.61849e9i	1.65326	−	0.417214i
$631$			9.61019e9i			1.52275i	0.648310	+	0.761376i	$0.275476\pi$
$631$			9.61019e9i			1.52275i	−0.648310	+	0.761376i	$0.724524\pi$
$632$	−8.11197e8	+	6.41796e9i	−0.127825	+	1.01132i
$633$	1.78615e8	+	3.11451e9i	0.0279902	+	0.488064i
$634$	−6.82213e9	+	5.25352e9i	−1.06318	+	0.818724i
$635$	4.64223e9	−	2.68019e9i	0.719480	−	0.415392i
$636$	−3.73302e9	−	1.11699e10i	−0.575388	−	1.72167i
$637$	−8.75383e8	−	5.05403e8i	−0.134187	−	0.0774728i
$638$	2.38353e9	−	3.17979e8i	0.363370	−	0.0484760i
$639$	5.41335e9	+	7.29851e9i	0.820755	+	1.10658i
$640$	−7.37089e9	−	5.51586e9i	−1.11145	−	0.831732i
$641$	8.57590e9	+	4.95130e9i	1.28611	+	0.742533i	0.977957	−	0.208805i	$-0.0669575\pi$
$641$	8.57590e9	+	4.95130e9i	1.28611	+	0.742533i	0.308148	+	0.951338i	$0.400291\pi$
$642$	−8.51957e9	+	7.37495e9i	−1.27071	+	1.09998i
$643$	−1.75057e9	−	3.03207e9i	−0.259681	−	0.449781i	0.706475	−	0.707738i	$-0.250284\pi$
$643$	−1.75057e9	−	3.03207e9i	−0.259681	−	0.449781i	−0.966156	+	0.257957i	$0.916951\pi$
$644$	8.01973e9	−	8.07522e9i	1.18320	−	1.19139i
$645$	1.47240e10	+	7.41111e9i	2.16056	+	1.08749i
$646$	1.39522e8	−	3.38485e8i	0.0203624	−	0.0493998i
$647$	8.22383e9			1.19374			0.596870	−	0.802338i	$-0.296411\pi$
$647$	8.22383e9			1.19374			0.596870	+	0.802338i	$0.296411\pi$
$648$	6.88947e9	−	7.15046e8i	0.994657	−	0.103234i
$649$	−2.38814e8			−0.0342928
$650$	−7.53528e8	+	1.82808e9i	−0.107622	+	0.261095i
$651$	5.84358e9	+	2.94128e9i	0.830128	+	0.417833i
$652$	8.87395e9	+	8.81297e9i	1.25386	+	1.24525i
$653$	9.06708e8	+	1.57046e9i	0.127430	+	0.220715i	0.922680	−	0.385566i	$-0.125994\pi$
$653$	9.06708e8	+	1.57046e9i	0.127430	+	0.220715i	−0.795250	+	0.606281i	$0.792661\pi$
$654$	−8.53717e9	+	7.39019e9i	−1.19342	+	1.03308i
$655$	−9.61216e9	−	5.54958e9i	−1.33652	−	0.771642i
$656$	2.01664e9	+	3.43795e9i	0.278910	+	0.475485i
$657$	−6.21665e9	−	8.38155e9i	−0.855219	−	1.15304i
$658$	−1.31533e10	+	1.75473e9i	−1.79988	+	0.240115i
$659$	−7.85695e8	−	4.53621e8i	−0.106944	−	0.0617440i	0.445574	−	0.895245i	$-0.353000\pi$
$659$	−7.85695e8	−	4.53621e8i	−0.106944	−	0.0617440i	−0.552518	+	0.833501i	$0.686333\pi$
$660$	7.88778e9	−	2.63613e9i	1.06795	−	0.356913i
$661$	−3.88159e9	+	2.24104e9i	−0.522762	+	0.301817i	−0.738064	−	0.674731i	$-0.764260\pi$
$661$	−3.88159e9	+	2.24104e9i	−0.522762	+	0.301817i	0.215302	+	0.976548i	$0.430927\pi$
$662$	−2.85522e9	+	2.19872e9i	−0.382505	+	0.294555i
$663$	6.64718e6	+	1.15907e8i	0.000885809	+	0.0154459i
$664$	1.22522e9	−	9.69362e9i	0.162415	−	1.28498i
$665$		−	1.36034e10i		−	1.79379i
$666$	−1.10747e9	+	2.79478e8i	−0.145268	+	0.0366596i
$667$	−4.73489e9			−0.617830
$668$	2.59793e9	−	9.83104e9i	0.337217	−	1.27609i
$669$	−6.68628e9	−	1.01858e10i	−0.863362	−	1.31523i
$670$	4.62385e9	−	3.56069e9i	0.593940	−	0.457375i
$671$	5.58393e9	+	9.67165e9i	0.713528	+	1.23587i
$672$	−9.47596e9	+	1.88938e9i	−1.20457	+	0.240174i
$673$	2.86284e9	−	4.95859e9i	0.362030	−	0.627055i	−0.626265	−	0.779611i	$-0.715417\pi$
$673$	2.86284e9	−	4.95859e9i	0.362030	−	0.627055i	0.988295	+	0.152556i	$0.0487504\pi$
$674$	1.48535e9	+	1.11340e10i	0.186861	+	1.40069i
$675$	−6.95427e9	−	2.55222e9i	−0.870339	−	0.319415i
$676$	−7.03172e9	+	1.91015e9i	−0.875484	+	0.237823i
$677$	4.69151e9	−	8.12594e9i	0.581102	−	1.00650i	−0.414247	−	0.910165i	$-0.635955\pi$
$677$	4.69151e9	−	8.12594e9i	0.581102	−	1.00650i	0.995349	−	0.0963341i	$-0.0307117\pi$
$678$	3.33456e9	+	1.15593e9i	0.410898	+	0.142439i
$679$	6.61403e9	−	3.81861e9i	0.810815	−	0.468124i
$680$	4.60460e8	+	3.49555e8i	0.0561579	+	0.0426319i
$681$	−3.23615e9	−	4.92989e9i	−0.392658	−	0.598167i
$682$	4.70052e9	+	1.93753e9i	0.567414	+	0.233886i
$683$		−	7.41864e9i		−	0.890947i	−0.895295	−	0.445473i	$-0.853035\pi$
$683$		−	7.41864e9i		−	0.890947i	0.895295	−	0.445473i	$-0.146965\pi$
$684$	1.26158e9	−	8.71394e9i	0.150737	−	1.04116i
$685$			5.31651e9i			0.631989i
$686$	1.94463e9	−	4.71773e9i	0.229986	−	0.557954i
$687$	−1.27032e10	+	7.28518e8i	−1.49473	+	0.0857219i
$688$	−1.29406e10	−	7.35277e9i	−1.51494	−	0.860779i
$689$	4.11138e9	−	2.37370e9i	0.478873	−	0.276477i
$690$	−1.60815e10	+	3.09128e9i	−1.86360	+	0.358234i
$691$	6.44224e9	−	1.11583e10i	0.742786	−	1.28654i	−0.208436	−	0.978036i	$-0.566837\pi$
$691$	6.44224e9	−	1.11583e10i	0.742786	−	1.28654i	0.951222	−	0.308508i	$-0.0998295\pi$
$692$	−1.10699e8	+	3.00710e7i	−0.0126990	+	0.00344966i
$693$	3.47158e9	−	8.00874e9i	0.396242	−	0.914109i
$694$	1.44537e9	−	1.92821e8i	0.164142	−	0.0218976i
$695$	−1.99823e9	+	3.46104e9i	−0.225787	+	0.391075i
$696$	3.33577e9	+	2.24336e9i	0.375028	+	0.252212i
$697$	−1.25144e8	−	2.16756e8i	−0.0139990	−	0.0242469i
$698$	1.92985e9	+	2.50608e9i	0.214798	+	0.278934i
$699$	3.26138e9	−	6.47953e9i	0.361186	−	0.717585i
$700$	9.99100e9	+	2.64020e9i	1.10095	+	0.290933i
$701$	−2.06922e9			−0.226879			−0.113440	−	0.993545i	$-0.536187\pi$
$701$	−2.06922e9			−0.226879			−0.113440	+	0.993545i	$0.536187\pi$
$702$	8.37065e8	+	2.66365e9i	0.0913228	+	0.290601i
$703$			1.45192e9i			0.157616i
$704$	−7.23287e9	+	2.01845e9i	−0.781280	+	0.218028i
$705$	1.70552e10	+	8.58446e9i	1.83313	+	0.922680i
$706$	6.08678e7	+	7.90419e7i	0.00650985	+	0.00845359i
$707$	−7.81563e9	+	4.51236e9i	−0.831756	+	0.480215i
$708$	−2.98916e8	−	2.64646e8i	−0.0316543	−	0.0280253i
$709$	4.10436e9	+	2.36965e9i	0.432498	+	0.249703i	0.700410	−	0.713741i	$-0.253000\pi$
$709$	4.10436e9	+	2.36965e9i	0.432498	+	0.249703i	−0.267912	+	0.963443i	$0.586334\pi$
$710$	2.41195e9	+	1.80797e10i	0.252909	+	1.89578i
$711$	−1.11687e9	−	9.70545e9i	−0.116536	−	1.01268i
$712$	3.67083e9	−	1.54280e9i	0.381140	−	0.160187i
$713$	−8.66980e9	−	5.00551e9i	−0.895768	−	0.517172i
$714$	5.95852e8	−	1.14539e8i	0.0612625	−	0.0117763i
$715$	1.67622e9	+	2.90331e9i	0.171499	+	0.297045i
$716$	1.33880e10	−	1.34806e10i	1.36308	−	1.37251i
$717$	−8.37299e8	−	1.46000e10i	−0.0848328	−	1.47923i
$718$	−4.57184e9	−	1.88449e9i	−0.460952	−	0.190002i
$719$	−3.88587e9			−0.389885			−0.194943	−	0.980815i	$-0.562452\pi$
$719$	−3.88587e9			−0.389885			−0.194943	+	0.980815i	$0.562452\pi$
$720$	1.27942e10	+	5.44145e9i	1.27746	+	0.543314i
$721$	1.06359e10			1.05682
$722$	−9.98006e8	−	4.11373e8i	−0.0986854	−	0.0406777i
$723$	−1.27712e10	+	8.38344e9i	−1.25674	+	0.824971i
$724$	2.38668e9	−	2.40320e9i	0.233728	−	0.235345i
$725$	−2.14965e9	−	3.72331e9i	−0.209501	−	0.362866i
$726$	−1.15515e9	+	3.33232e9i	−0.112037	+	0.323198i
$727$	9.55281e9	+	5.51532e9i	0.922063	+	0.532353i	0.884293	−	0.466933i	$-0.154641\pi$
$727$	9.55281e9	+	5.51532e9i	0.922063	+	0.532353i	0.0377703	+	0.999286i	$0.487974\pi$
$728$	−1.50913e9	−	3.59072e9i	−0.144966	−	0.344923i
$729$	−9.84850e9	+	3.52505e9i	−0.941508	+	0.336991i
$730$	−2.76986e9	−	2.07626e10i	−0.263529	−	1.97538i
$731$	8.09411e8	+	4.67314e8i	0.0766405	+	0.0442484i
$732$	−3.72860e9	+	1.82936e10i	−0.351363	+	1.72390i
$733$	5.86289e9	−	3.38494e9i	0.549855	−	0.317459i	−0.199209	−	0.979957i	$-0.563837\pi$
$733$	5.86289e9	−	3.38494e9i	0.549855	−	0.317459i	0.749063	+	0.662498i	$0.230504\pi$
$734$	1.20449e9	+	1.56413e9i	0.112426	+	0.145995i
$735$	6.35454e9	−	4.17134e9i	0.590308	−	0.387499i
$736$	1.46424e10	−	2.05625e9i	1.35375	−	0.190109i
$737$		−	4.76021e9i		−	0.438016i
$738$	−4.19368e9	−	4.31798e9i	−0.384059	−	0.395443i
$739$	6.52162e9			0.594429			0.297215	−	0.954811i	$-0.403942\pi$
$739$	6.52162e9			0.594429			0.297215	+	0.954811i	$0.403942\pi$
$740$	−2.21658e9	−	5.85747e8i	−0.201081	−	0.0531372i
$741$	3.54341e9	−	2.03212e8i	0.319932	−	0.0183479i
$742$	−1.51382e10	−	1.96582e10i	−1.36038	−	1.76656i
$743$	−2.50058e9	−	4.33113e9i	−0.223655	−	0.387383i	0.732260	−	0.681025i	$-0.238466\pi$
$743$	−2.50058e9	−	4.33113e9i	−0.223655	−	0.387383i	−0.955915	+	0.293643i	$0.905132\pi$
$744$	3.73638e9	+	7.63412e9i	0.332618	+	0.679600i
$745$	9.77542e9	−	1.69315e10i	0.866141	−	1.50020i
$746$	4.85943e9	−	6.48280e8i	0.428548	−	0.0571711i
$747$	1.68692e9	+	1.46590e10i	0.148072	+	1.28672i
$748$	4.55055e8	−	1.23615e8i	0.0397565	−	0.0107998i
$749$	−1.18696e10	+	2.05587e10i	−1.03217	+	1.78776i
$750$	7.65228e8	+	8.83995e8i	0.0662333	+	0.0765130i
$751$	5.85492e8	−	3.38034e8i	0.0504407	−	0.0291220i	−0.474568	−	0.880219i	$-0.657396\pi$
$751$	5.85492e8	−	3.38034e8i	0.0504407	−	0.0291220i	0.525008	+	0.851097i	$0.324062\pi$
$752$	−1.49894e10	−	8.51689e9i	−1.28535	−	0.730329i
$753$	−6.36570e9	+	1.26470e10i	−0.543330	+	1.07946i
$754$	−6.17538e8	+	1.49817e9i	−0.0524643	+	0.127280i
$755$		−	1.87215e10i		−	1.58316i
$756$	1.32203e10	−	6.17720e9i	1.11279	−	0.519954i
$757$			7.58307e9i			0.635345i	0.948200	+	0.317673i	$0.102901\pi$
$757$			7.58307e9i			0.635345i	−0.948200	+	0.317673i	$0.897099\pi$
$758$	−8.72235e9	−	3.59531e9i	−0.727430	−	0.299844i
$759$	−6.00537e9	+	1.19312e10i	−0.498532	+	0.990458i
$760$	1.06863e10	−	1.40768e10i	0.883038	−	1.16320i
$761$	1.26841e10	−	7.32319e9i	1.04331	−	0.602357i	0.122543	−	0.992463i	$-0.460895\pi$
$761$	1.26841e10	−	7.32319e9i	1.04331	−	0.602357i	0.920770	+	0.390106i	$0.127562\pi$
$762$	5.52638e9	−	4.78390e9i	0.452479	−	0.391687i
$763$	−1.18941e10	+	2.06012e10i	−0.969385	+	1.67902i
$764$	−1.46795e10	+	3.98764e9i	−1.19092	+	0.323511i
$765$	−8.01042e8	−	3.47230e8i	−0.0646904	−	0.0280416i
$766$	7.24402e8	+	5.43003e9i	0.0582343	+	0.436518i
$767$	8.04662e7	−	1.39371e8i	0.00643916	−	0.0111530i
$768$	−1.12899e10	−	5.48882e9i	−0.899347	−	0.437235i
$769$	1.12599e9	+	1.95027e9i	0.0892877	+	0.154651i	0.907210	−	0.420678i	$-0.138208\pi$
$769$	1.12599e9	+	1.95027e9i	0.0892877	+	0.154651i	−0.817923	+	0.575328i	$0.804874\pi$
$770$	1.38819e10	−	1.06900e10i	1.09580	−	0.843842i
$771$	−1.77401e10	+	1.01738e9i	−1.39401	+	0.0799455i
$772$	−2.49602e8	+	9.44543e8i	−0.0195249	+	0.0738858i
$773$	6.39825e9			0.498233			0.249117	−	0.968473i	$-0.419860\pi$
$773$	6.39825e9			0.498233			0.249117	+	0.968473i	$0.419860\pi$
$774$	2.16241e10	+	6.13396e9i	1.67627	+	0.475497i
$775$		−	9.09007e9i		−	0.701474i
$776$	9.84394e9	+	1.24422e9i	0.756228	+	0.0955834i
$777$	−2.01160e9	+	1.32048e9i	−0.153840	+	0.100986i
$778$	−2.26296e9	+	1.74264e9i	−0.172285	+	0.132672i
$779$	−6.62648e9	+	3.82580e9i	−0.502229	+	0.289962i
$780$	−1.11928e9	+	5.49152e9i	−0.0844513	+	0.414344i
$781$	1.28844e10	+	7.43884e9i	0.967803	+	0.558762i
$782$	−9.20346e8	+	1.22780e8i	−0.0688220	+	0.00918131i
$783$	−5.69923e9	−	2.09162e9i	−0.424278	−	0.155710i
$784$	−5.92006e9	+	3.47259e9i	−0.438753	+	0.257364i
$785$	1.58490e10	+	9.15042e9i	1.16939	+	0.675145i
$786$	−1.42998e10	−	4.95706e9i	−1.05039	−	0.364120i
$787$	1.87260e9	+	3.24343e9i	0.136941	+	0.237188i	0.926337	−	0.376695i	$-0.122940\pi$
$787$	1.87260e9	+	3.24343e9i	0.136941	+	0.237188i	−0.789396	+	0.613884i	$0.789606\pi$
$788$	5.33765e9	+	5.30097e9i	0.388605	+	0.385935i
$789$	−4.14749e8	+	2.72255e8i	−0.0300618	+	0.0197336i
$790$	7.47315e9	−	1.81301e10i	0.539273	−	1.30829i
$791$	7.43515e9			0.534161
$792$	9.88374e9	−	5.56031e9i	0.706941	−	0.397705i
$793$	−7.52581e9			−0.535917
$794$	2.17932e9	−	5.28711e9i	0.154508	−	0.374841i
$795$	2.04406e9	+	3.56423e10i	0.144281	+	2.51583i
$796$	−6.36475e9	+	6.40879e9i	−0.447286	+	0.450381i
$797$	1.16262e10	+	2.01371e10i	0.813452	+	1.40894i	0.910434	+	0.413654i	$0.135748\pi$
$797$	1.16262e10	+	2.01371e10i	0.813452	+	1.40894i	−0.0969818	+	0.995286i	$0.530919\pi$
$798$	−3.50158e9	−	1.82159e10i	−0.243923	−	1.26894i
$799$	9.37560e8	+	5.41300e8i	0.0650257	+	0.0375426i
$800$	8.26465e9	+	1.05806e10i	0.570702	+	0.730627i
$801$	−4.82987e9	+	3.58235e9i	−0.332064	+	0.246294i
$802$	1.86935e9	−	2.49384e8i	0.127962	−	0.0170710i
$803$	−1.47964e10	−	8.54270e9i	−1.00844	−	0.582225i
$804$	5.27512e9	−	5.95821e9i	0.357961	−	0.404315i
$805$	−2.98776e10	+	1.72498e10i	−2.01864	+	1.16546i
$806$	−2.71454e9	+	2.09038e9i	−0.182609	+	0.140622i
$807$	−1.05993e10	−	5.33500e9i	−0.709937	−	0.357336i
$808$	−1.16323e10	−	1.47027e9i	−0.775760	−	0.0980521i
$809$			4.31626e9i			0.286608i	0.989679	+	0.143304i	$0.0457726\pi$
$809$			4.31626e9i			0.286608i	−0.989679	+	0.143304i	$0.954227\pi$
$810$	−2.07223e10	−	3.38305e9i	−1.37006	−	0.223672i
$811$	3.66581e9			0.241322			0.120661	−	0.992694i	$-0.461499\pi$
$811$	3.66581e9			0.241322			0.120661	+	0.992694i	$0.461499\pi$
$812$	8.18791e9	+	2.16372e9i	0.536695	+	0.141826i
$813$	−6.46377e9	+	1.28419e10i	−0.421860	+	0.838130i
$814$	−1.48165e9	+	1.14097e9i	−0.0962852	+	0.0741463i
$815$	−1.89560e10	−	3.28328e10i	−1.22658	−	2.12450i
$816$	7.06565e8	+	3.49554e8i	0.0455236	+	0.0225216i
$817$	1.42863e10	−	2.47446e10i	0.916522	−	1.58746i
$818$	2.23681e8	+	1.67669e9i	0.0142887	+	0.107107i
$819$	3.50417e9	+	4.72448e9i	0.222891	+	0.300511i
$820$	−3.16734e9	−	1.16597e10i	−0.200607	−	0.738483i
$821$	1.85918e9	−	3.22019e9i	0.117252	−	0.203086i	−0.801426	−	0.598094i	$-0.795925\pi$
$821$	1.85918e9	−	3.22019e9i	0.117252	−	0.203086i	0.918678	+	0.395008i	$0.129258\pi$
$822$	1.36849e9	+	7.11917e9i	0.0859392	+	0.447073i
$823$	1.40095e10	−	8.08841e9i	0.876041	−	0.505782i	0.00668993	−	0.999978i	$-0.497871\pi$
$823$	1.40095e10	−	8.08841e9i	0.876041	−	0.505782i	0.869351	+	0.494195i	$0.164537\pi$
$824$	1.10060e10	+	8.35513e9i	0.685306	+	0.520245i
$825$	−1.21086e10	+	6.94420e8i	−0.750767	+	0.0430560i
$826$	−7.77613e8	−	3.20528e8i	−0.0480102	−	0.0197896i
$827$		−	1.09744e9i		−	0.0674699i	−0.999431	−	0.0337350i	$-0.989260\pi$
$827$		−	1.09744e9i		−	0.0674699i	0.999431	−	0.0337350i	$-0.0107402\pi$
$828$	−2.07385e10	+	8.27888e9i	−1.26961	+	0.506834i
$829$		−	2.38727e10i		−	1.45533i	−0.685935	−	0.727663i	$-0.740607\pi$
$829$		−	2.38727e10i		−	1.45533i	0.685935	−	0.727663i	$-0.259393\pi$
$830$	−1.12874e10	+	2.73835e10i	−0.685203	+	1.66233i
$831$	2.08570e9	+	3.17731e9i	0.126080	+	0.192068i
$832$	1.25909e9	−	4.90119e9i	0.0757921	−	0.295033i
$833$	3.73248e8	−	2.15495e8i	0.0223738	−	0.0129175i
$834$	−1.78488e9	+	5.14893e9i	−0.106544	+	0.307352i
$835$	−1.54122e10	+	2.66947e10i	−0.916140	+	1.58680i
$836$	−3.77904e9	−	1.39116e10i	−0.223697	−	0.823482i
$837$	−8.22439e9	−	9.85483e9i	−0.484802	−	0.580911i
$838$	−1.30556e10	+	1.74170e9i	−0.766378	+	0.102240i
$839$	3.30294e9	−	5.72085e9i	0.193078	−	0.334421i	−0.753191	−	0.657802i	$-0.771486\pi$
$839$	3.30294e9	−	5.72085e9i	0.193078	−	0.334421i	0.946269	+	0.323381i	$0.104820\pi$
$840$	2.92219e10	+	2.00312e9i	1.70110	+	0.116609i
$841$	6.86323e9	+	1.18875e10i	0.397871	+	0.689134i
$842$	1.18503e10	+	1.53886e10i	0.684126	+	0.888395i
$843$	−8.25187e9	−	1.25707e10i	−0.474412	−	0.722710i
$844$	−2.18151e9	+	8.25526e9i	−0.124899	+	0.472642i
$845$	2.20881e10			1.25939
$846$	2.50477e10	+	7.10511e9i	1.42224	+	0.403436i
$847$			7.43016e9i			0.420152i
$848$	−2.22267e8	−	3.22342e10i	−0.0125167	−	1.81523i
$849$	3.99024e8	+	6.95777e9i	0.0223780	+	0.390206i
$850$	−5.14389e8	−	6.67978e8i	−0.0287293	−	0.0373075i
$851$	3.18891e9	−	1.84112e9i	0.177373	−	0.102407i
$852$	7.88357e9	+	2.35891e10i	0.436701	+	1.30669i
$853$	−2.39546e10	−	1.38302e10i	−1.32150	−	0.762968i	−0.337531	−	0.941314i	$-0.609592\pi$
$853$	−2.39546e10	−	1.38302e10i	−1.32150	−	0.762968i	−0.983968	+	0.178346i	$0.942925\pi$
$854$	5.20110e9	+	3.89869e10i	0.285754	+	2.14198i
$855$	−1.06152e10	+	2.44888e10i	−0.580828	+	1.33994i
$856$	−2.84328e10	+	1.19499e10i	−1.54939	+	0.651187i
$857$	5.16418e9	+	2.98154e9i	0.280265	+	0.161811i	0.633543	−	0.773707i	$-0.281600\pi$
$857$	5.16418e9	+	2.98154e9i	0.280265	+	0.161811i	−0.353279	+	0.935518i	$0.614933\pi$
$858$	2.99190e9	+	3.45626e9i	0.161712	+	0.186810i
$859$	9.54852e9	+	1.65385e10i	0.513996	+	0.890268i	0.999868	+	0.0162376i	$0.00516880\pi$
$859$	9.54852e9	+	1.65385e10i	0.513996	+	0.890268i	−0.485872	+	0.874030i	$0.661498\pi$
$860$	3.20128e10	+	3.17929e10i	1.71625	+	1.70445i
$861$	−1.13271e10	−	5.70135e9i	−0.604797	−	0.304416i
$862$	4.18113e9	+	1.72344e9i	0.222340	+	0.0916477i
$863$	4.06829e9			0.215464			0.107732	−	0.994180i	$-0.465641\pi$
$863$	4.06829e9			0.215464			0.107732	+	0.994180i	$0.465641\pi$
$864$	1.85329e10	+	3.99319e9i	0.977566	+	0.210631i
$865$	3.47728e8			0.0182677
$866$	2.44285e10	+	1.00693e10i	1.27816	+	0.526851i
$867$	1.70966e10	+	8.60532e9i	0.890928	+	0.448436i
$868$	1.27051e10	+	1.26178e10i	0.659414	+	0.654882i
$869$	−7.99759e9	−	1.38522e10i	−0.413419	−	0.716062i
$870$	−7.97557e9	−	9.21341e9i	−0.410624	−	0.474354i
$871$	2.77805e9	+	1.60391e9i	0.142455	+	0.0822463i
$872$	−2.84915e10	+	1.19746e10i	−1.45515	+	0.611579i
$873$	−1.48863e10	+	1.71308e9i	−0.757248	+	0.0871419i
$874$	3.75353e9	+	2.81360e10i	0.190173	+	1.42552i
$875$	2.13318e9	+	1.23159e9i	0.107647	+	0.0621498i
$876$	−9.05342e9	−	2.70895e10i	−0.455039	−	1.36156i
$877$	1.92645e10	−	1.11224e10i	0.964404	−	0.556799i	0.0668783	−	0.997761i	$-0.478696\pi$
$877$	1.92645e10	−	1.11224e10i	0.964404	−	0.556799i	0.897526	+	0.440962i	$0.145363\pi$
$878$	−8.46397e9	−	1.09912e10i	−0.422030	−	0.548041i
$879$	−1.03725e7	−	1.80866e8i	−0.000515138	−	0.00898246i
$880$	2.27626e10	−	1.56957e8i	1.12599	−	0.00776411i
$881$			2.93010e9i			0.144366i	0.997391	+	0.0721832i	$0.0229966\pi$
$881$			2.93010e9i			0.144366i	−0.997391	+	0.0721832i	$0.977003\pi$
$882$	7.43545e9	−	7.22140e9i	0.364894	−	0.354390i
$883$	−1.88410e10			−0.920961			−0.460481	−	0.887670i	$-0.652323\pi$
$883$	−1.88410e10			−0.920961			−0.460481	+	0.887670i	$0.652323\pi$
$884$	−8.11853e7	+	3.07220e8i	−0.00395270	+	0.0149578i
$885$	6.64128e8	+	1.01172e9i	0.0322070	+	0.0490635i
$886$	−2.20406e10	−	2.86215e10i	−1.06464	−	1.38253i
$887$	7.27997e9	+	1.26093e10i	0.350265	+	0.606677i	0.986296	−	0.164987i	$-0.0527582\pi$
$887$	7.27997e9	+	1.26093e10i	0.350265	+	0.606677i	−0.636031	+	0.771664i	$0.719425\pi$
$888$	−3.11892e9	−	2.13798e8i	−0.149472	−	0.0102461i
$889$	7.69943e9	−	1.33358e10i	0.367538	−	0.636595i
$890$	−1.19644e10	+	1.59614e9i	−0.568889	+	0.0758935i
$891$	−1.24990e10	+	1.17083e10i	−0.591976	+	0.554526i
$892$	−8.74239e9	−	3.21828e10i	−0.412433	−	1.51826i
$893$	1.65482e10	−	2.86623e10i	0.777624	−	1.34689i
$894$	8.73171e9	−	2.51887e10i	0.408712	−	1.17903i
$895$	−4.98771e10	+	2.87965e10i	−2.32552	+	1.34264i
$896$	−2.62604e10	−	3.13537e9i	−1.21962	−	0.145617i
$897$	−4.93955e9	−	7.52482e9i	−0.228514	−	0.348115i
$898$	−1.96147e9	+	4.75859e9i	−0.0903888	+	0.219286i
$899$		−	7.44958e9i		−	0.341958i
$900$	−1.59255e10	−	1.25492e10i	−0.728189	−	0.573809i
$901$			2.02421e9i			0.0921976i
$902$	−9.11145e9	−	3.75570e9i	−0.413394	−	0.170399i
$903$	4.72760e10	−	2.71125e9i	2.13665	−	0.122535i
$904$	7.69389e9	+	5.84077e9i	0.346383	+	0.262954i
$905$	−8.89161e9	+	5.13357e9i	−0.398759	+	0.230223i
$906$	−4.81899e9	−	2.50693e10i	−0.215282	−	1.11994i
$907$	−2.73146e9	+	4.73103e9i	−0.121554	+	0.210538i	−0.920381	−	0.391023i	$-0.872121\pi$
$907$	−2.73146e9	+	4.73103e9i	−0.121554	+	0.210538i	0.798827	+	0.601561i	$0.205454\pi$
$908$	−4.23131e9	−	1.55765e10i	−0.187575	−	0.690507i
$909$	1.75908e10	−	2.02430e9i	0.776805	−	0.0893925i
$910$	1.56130e9	+	1.17034e10i	0.0686820	+	0.514832i
$911$	−1.10009e10	+	1.90542e10i	−0.482076	+	0.834981i	−0.999788	−	0.0205743i	$-0.993451\pi$
$911$	−1.10009e10	+	1.90542e10i	−0.482076	+	0.834981i	0.517712	+	0.855555i	$0.326784\pi$
$912$	1.06863e10	−	2.16005e10i	0.466491	−	0.942935i
$913$	1.20795e10	+	2.09223e10i	0.525292	+	0.909832i
$914$	3.19470e10	−	2.46014e10i	1.38394	−	1.06573i
$915$	2.54447e10	−	5.05522e10i	1.09805	−	2.18156i
$916$	−3.36708e10	−	8.89775e9i	−1.44750	−	0.382513i
$917$	−3.18847e10			−1.36549
$918$	−1.16203e9	−	2.58773e8i	−0.0495755	−	0.0110400i
$919$		−	9.87478e9i		−	0.419685i	−0.977735	−	0.209842i	$-0.932705\pi$
$919$		−	9.87478e9i		−	0.419685i	0.977735	−	0.209842i	$-0.0672951\pi$
$920$	−4.44681e10	−	5.62054e9i	−1.88274	−	0.237969i
$921$	−1.19389e10	−	6.00926e9i	−0.503565	−	0.253462i
$922$	2.83382e10	−	2.18224e10i	1.19073	−	0.916947i
$923$	−8.68259e9	+	5.01290e9i	−0.363449	+	0.209837i
$924$	1.58371e10	−	1.78879e10i	0.660427	−	0.745948i
$925$	2.89555e9	+	1.67175e9i	0.120292	+	0.0694503i
$926$	−3.66935e10	+	4.89516e9i	−1.51863	+	0.202595i
$927$	−1.91467e10	−	8.29956e9i	−0.789431	−	0.342197i
$928$	6.77312e9	+	8.67112e9i	0.278209	+	0.356170i
$929$	1.44832e10	+	8.36187e9i	0.592665	+	0.342175i	0.766151	−	0.642661i	$-0.222170\pi$
$929$	1.44832e10	+	8.36187e9i	0.592665	+	0.342175i	−0.173486	+	0.984836i	$0.555503\pi$
$930$	−4.86364e9	−	2.53016e10i	−0.198276	−	1.03147i
$931$	−6.58793e9	−	1.14106e10i	−0.267562	−	0.463431i
$932$	1.39909e10	−	1.40878e10i	0.566098	−	0.570015i
$933$	1.48051e9	+	2.58156e10i	0.0596795	+	1.04063i
$934$	2.98305e9	−	7.23698e9i	0.119797	−	0.290632i
$935$	−1.42943e9			−0.0571901
$936$	−8.52468e7	+	7.64163e9i	−0.00339792	+	0.304593i
$937$	−1.89555e10			−0.752742			−0.376371	−	0.926469i	$-0.622828\pi$
$937$	−1.89555e10			−0.752742			−0.376371	+	0.926469i	$0.622828\pi$
$938$	6.38900e9	−	1.54999e10i	0.252769	−	0.613225i
$939$	7.37670e9	−	4.84232e9i	0.290759	−	0.190864i
$940$	3.70812e10	+	3.68264e10i	1.45615	+	1.44615i
$941$	1.99094e10	+	3.44840e10i	0.778921	+	1.34913i	0.932564	+	0.361005i	$0.117566\pi$
$941$	1.99094e10	+	3.44840e10i	0.778921	+	1.34913i	−0.153643	+	0.988126i	$0.549100\pi$
$942$	2.35783e10	+	8.17344e9i	0.919038	+	0.318586i
$943$	1.68055e10	+	9.70264e9i	0.652619	+	0.376790i
$944$	−5.52879e8	−	9.42545e8i	−0.0213908	−	0.0364670i
$945$	−4.35827e10	+	7.56474e9i	−1.67998	+	0.291597i
$946$	3.64779e10	−	4.86639e9i	1.40091	−	0.186891i
$947$	−2.04655e10	−	1.18157e10i	−0.783063	−	0.452101i	0.0544519	−	0.998516i	$-0.482659\pi$
$947$	−2.04655e10	−	1.18157e10i	−0.783063	−	0.452101i	−0.837515	+	0.546415i	$0.815992\pi$
$948$	5.34029e9	−	2.62011e10i	0.203580	−	0.998827i
$949$	9.97101e9	−	5.75676e9i	0.378711	−	0.218649i
$950$	−2.04208e10	+	1.57255e10i	−0.772754	+	0.595074i
$951$	2.97538e10	−	1.95314e10i	1.12179	−	0.736381i
$952$	1.64764e9	+	2.08253e8i	0.0618917	+	0.00782280i
$953$			3.20347e10i			1.19893i	0.800400	+	0.599467i	$0.204621\pi$
$953$			3.20347e10i			1.19893i	−0.800400	+	0.599467i	$0.795379\pi$
$954$	1.19116e10	+	4.72014e10i	0.444173	+	1.76009i
$955$	4.61113e10			1.71315
$956$	1.02263e10	−	3.86984e10i	0.378545	−	1.43249i
$957$	−9.92336e9	+	5.69098e8i	−0.365988	+	0.0209892i
$958$	1.39940e10	−	1.07764e10i	0.514237	−	0.395998i
$959$	7.63640e9	+	1.32266e10i	0.279591	+	0.484266i
$960$	2.86652e10	+	2.50284e10i	1.04570	+	0.913027i
$961$	−5.88094e9	+	1.01861e10i	−0.213754	+	0.370233i
$962$	−1.66642e8	−	1.24913e9i	−0.00603492	−	0.0452370i
$963$	3.74103e10	−	2.77474e10i	1.34989	−	1.00122i
$964$	−4.03517e10	+	1.09615e10i	−1.45075	+	0.394093i
$965$	1.48077e9	−	2.56476e9i	0.0530446	−	0.0918759i
$966$	−3.55680e10	+	3.07893e10i	−1.26952	+	1.09896i
$967$	−9.32310e9	+	5.38269e9i	−0.331564	+	0.191429i	−0.656535	−	0.754295i	$-0.727979\pi$
$967$	−9.32310e9	+	5.38269e9i	−0.331564	+	0.191429i	0.324971	+	0.945724i	$0.394645\pi$
$968$	−5.83684e9	+	7.68872e9i	−0.206830	+	0.272452i
$969$	−6.80386e8	+	1.35176e9i	−0.0240227	+	0.0477271i
$970$	−2.78082e10	−	1.14624e10i	−0.978299	−	0.403250i
$971$		−	3.42587e10i		−	1.20089i	−0.799665	−	0.600446i	$-0.794990\pi$
$971$		−	3.42587e10i		−	1.20089i	0.799665	−	0.600446i	$-0.205010\pi$
$972$	−2.86194e10	+	8.03874e8i	−0.999606	+	0.0280774i
$973$			1.14807e10i			0.399552i
$974$	5.00189e9	−	1.21347e10i	0.173451	−	0.420799i
$975$	3.67462e9	−	7.30054e9i	0.126969	−	0.252255i
$976$	−2.52444e10	+	4.44294e10i	−0.869143	+	1.52966i
$977$	−1.87509e10	+	1.08258e10i	−0.643267	+	0.371390i	−0.785872	−	0.618389i	$-0.787785\pi$
$977$	−1.87509e10	+	1.08258e10i	−0.643267	+	0.371390i	0.142605	+	0.989780i	$0.454452\pi$
$978$	−3.38347e10	−	3.90860e10i	−1.15658	−	1.33609i
$979$	−4.92273e9	+	8.52643e9i	−0.167675	+	0.290421i
$980$	2.00778e10	−	5.45408e9i	0.681434	−	0.185110i
$981$	3.74876e10	−	2.78048e10i	1.26779	−	0.940325i
$982$	2.98834e10	−	3.98664e9i	1.00702	−	0.134343i
$983$	−8.91156e9	+	1.54353e10i	−0.299238	+	0.518295i	−0.975962	−	0.217942i	$-0.930066\pi$
$983$	−8.91156e9	+	1.54353e10i	−0.299238	+	0.518295i	0.676724	+	0.736237i	$0.263399\pi$
$984$	−7.24257e9	−	1.47979e10i	−0.242331	−	0.495128i
$985$	−1.14020e10	−	1.97488e10i	−0.380149	−	0.658437i
$986$	−4.21557e8	−	5.47427e8i	−0.0140051	−	0.0181868i
$987$	5.47609e10	−	3.14050e9i	1.81284	−	0.103965i
$988$	9.39208e9	+	2.48193e9i	0.309822	+	0.0818728i
$989$	−7.24632e10			−2.38194
$990$	−3.33319e10	+	8.41157e9i	−1.09178	+	0.275521i
$991$		−	3.95487e10i		−	1.29085i	−0.763825	−	0.645423i	$-0.776681\pi$
$991$		−	3.95487e10i		−	1.29085i	0.763825	−	0.645423i	$-0.223319\pi$
$992$	3.23518e9	+	2.30375e10i	0.105222	+	0.749279i
$993$	1.24527e10	−	8.17436e9i	0.403590	−	0.264930i
$994$	3.19694e10	+	4.15150e10i	1.03248	+	1.34077i
$995$	2.37119e10	−	1.36901e10i	0.763108	−	0.440580i
$996$	−8.06592e9	+	3.95739e10i	−0.258670	+	1.26911i
$997$	2.20869e10	+	1.27519e10i	0.705833	+	0.407513i	0.809516	−	0.587098i	$-0.199730\pi$
$997$	2.20869e10	+	1.27519e10i	0.705833	+	0.407513i	−0.103683	+	0.994610i	$0.533063\pi$
$998$	3.59748e9	+	2.69663e10i	0.114562	+	0.858745i
$999$	4.65169e9	−	8.07403e8i	0.147615	−	0.0256219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.8.l.b.11.10	✓	160
8.3	odd	2	inner	72.8.l.b.11.18	yes	160
9.5	odd	6	inner	72.8.l.b.59.18	yes	160
72.59	even	6	inner	72.8.l.b.59.10	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.8.l.b.11.10	✓	160	1.1	even	1	trivial
72.8.l.b.11.18	yes	160	8.3	odd	2	inner
72.8.l.b.59.10	yes	160	72.59	even	6	inner
72.8.l.b.59.18	yes	160	9.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	72.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.4600 - 4.31154i) q^{2} +(41.7723 + 21.0255i) q^{3} +(90.8212 + 90.1971i) q^{4} +(-194.007 - 336.030i) q^{5} +(-346.284 - 400.029i) q^{6} +(-965.318 - 557.326i) q^{7} +(-561.096 - 1335.04i) q^{8} +(1302.86 + 1756.57i) q^{9} +O(q^{10})\)	\(q+(-10.4600 - 4.31154i) q^{2} +(41.7723 + 21.0255i) q^{3} +(90.8212 + 90.1971i) q^{4} +(-194.007 - 336.030i) q^{5} +(-346.284 - 400.029i) q^{6} +(-965.318 - 557.326i) q^{7} +(-561.096 - 1335.04i) q^{8} +(1302.86 + 1756.57i) q^{9} +(580.496 + 4351.33i) q^{10} +(3100.96 + 1790.34i) q^{11} +(1897.38 + 5677.30i) q^{12} +(-2089.68 + 1206.48i) q^{13} +(7694.24 + 9991.62i) q^{14} +(-1038.93 - 18115.8i) q^{15} +(112.971 + 16383.6i) q^{16} -1028.84i q^{17} +(-6054.30 - 23990.9i) q^{18} -31452.9 q^{19} +(12689.0 - 48017.5i) q^{20} +(-28605.5 - 43577.1i) q^{21} +(-24716.8 - 32096.8i) q^{22} +(39883.9 + 69081.0i) q^{23} +(4631.49 - 67564.9i) q^{24} +(-36214.9 + 62726.0i) q^{25} +(27059.7 - 3609.95i) q^{26} +(17490.7 + 100769. i) q^{27} +(-37402.1 - 137686. i) q^{28} +(-29679.2 + 51405.8i) q^{29} +(-67240.1 + 193970. i) q^{30} +(-108688. + 62751.0i) q^{31} +(69457.0 - 171859. i) q^{32} +(91891.6 + 139986. i) q^{33} +(-4435.90 + 10761.6i) q^{34} +432501. i q^{35} +(-40110.3 + 277048. i) q^{36} -46161.9i q^{37} +(328996. + 135610. i) q^{38} +(-112658. + 6460.84i) q^{39} +(-339756. + 447552. i) q^{40} +(210680. - 121636. i) q^{41} +(111328. + 579148. i) q^{42} +(-454213. + 786720. i) q^{43} +(120149. + 442298. i) q^{44} +(337496. - 778585. i) q^{45} +(-119338. - 894545. i) q^{46} +(-526126. + 911277. i) q^{47} +(-339754. + 686757. i) q^{48} +(209454. + 362785. i) q^{49} +(649252. - 499969. i) q^{50} +(21631.9 - 42977.2i) q^{51} +(-298608. - 78909.4i) q^{52} -1.96747e6 q^{53} +(251519. - 1.12945e6i) q^{54} -1.38935e6i q^{55} +(-202415. + 1.60145e6i) q^{56} +(-1.31386e6 - 661312. i) q^{57} +(532081. - 409739. i) q^{58} +(-57759.7 + 33347.6i) q^{59} +(1.53964e6 - 1.73901e6i) q^{60} +(2.70106e6 + 1.55946e6i) q^{61} +(1.40742e6 - 187760. i) q^{62} +(-278689. - 2.42176e6i) q^{63} +(-1.46749e6 + 1.49817e6i) q^{64} +(810825. + 468130. i) q^{65} +(-357626. - 1.86044e6i) q^{66} +(-664708. - 1.15131e6i) q^{67} +(92798.6 - 93440.7i) q^{68} +(213583. + 3.72425e6i) q^{69} +(1.86475e6 - 4.52394e6i) q^{70} +4.15499e6 q^{71} +(1.61405e6 - 2.72497e6i) q^{72} -4.77155e6 q^{73} +(-199029. + 482851. i) q^{74} +(-2.83163e6 + 1.85878e6i) q^{75} +(-2.85659e6 - 2.83696e6i) q^{76} +(-1.99561e6 - 3.45649e6i) q^{77} +(1.20625e6 + 418148. i) q^{78} +(-3.86860e6 - 2.23354e6i) q^{79} +(5.48347e6 - 3.21650e6i) q^{80} +(-1.38809e6 + 4.57712e6i) q^{81} +(-2.72814e6 + 363952. i) q^{82} +(5.84310e6 + 3.37351e6i) q^{83} +(1.33254e6 - 6.53786e6i) q^{84} +(-345722. + 199603. i) q^{85} +(8.14303e6 - 6.27070e6i) q^{86} +(-2.32060e6 + 1.52332e6i) q^{87} +(650232. - 5.14445e6i) q^{88} +2.74961e6i q^{89} +(-6.88710e6 + 6.68884e6i) q^{90} +2.68961e6 q^{91} +(-2.60860e6 + 9.87143e6i) q^{92} +(-5.85952e6 + 336039. i) q^{93} +(9.43226e6 - 7.26349e6i) q^{94} +(6.10208e6 + 1.05691e7i) q^{95} +(6.51480e6 - 5.71858e6i) q^{96} +(-3.42583e6 + 5.93371e6i) q^{97} +(-626715. - 4.69778e6i) q^{98} +(895255. + 7.77961e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9}+O(q^{10}) \) 160 * q - 3 * q^2 - 90 * q^3 - 257 * q^4 - 459 * q^6 + 3018 * q^9	\( 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9} + 252 q^{10} - 26448 q^{11} - 27234 q^{12} - 43488 q^{14} + 32767 q^{16} + 21762 q^{18} - 119452 q^{19} + 130806 q^{20} - 6049 q^{22} - 83379 q^{24} - 1312502 q^{25} - 94428 q^{27} - 32772 q^{28} + 735060 q^{30} + 308907 q^{32} - 1249812 q^{33} - 188203 q^{34} - 1410345 q^{36} + 353415 q^{38} - 477876 q^{40} - 1612476 q^{41} - 39360 q^{42} + 220508 q^{43} + 1082496 q^{46} - 3515619 q^{48} + 9882514 q^{49} - 136947 q^{50} - 2358786 q^{51} + 1089018 q^{52} - 8083005 q^{54} - 1285266 q^{56} - 2070294 q^{57} + 1295022 q^{58} - 8748744 q^{59} - 3070044 q^{60} + 16058050 q^{64} - 6 q^{65} - 19546374 q^{66} + 3851300 q^{67} + 10545975 q^{68} + 979920 q^{70} + 12593427 q^{72} - 9731236 q^{73} + 13246572 q^{74} + 8347746 q^{75} - 4009903 q^{76} - 9123732 q^{78} - 6855198 q^{81} + 21020522 q^{82} - 14348826 q^{83} + 44644836 q^{84} + 80099985 q^{86} + 10463891 q^{88} + 7437678 q^{90} - 3294180 q^{91} - 57890184 q^{92} - 1609122 q^{94} + 69780834 q^{96} + 9938888 q^{97} - 16049670 q^{99}+O(q^{100}) \) 160 * q - 3 * q^2 - 90 * q^3 - 257 * q^4 - 459 * q^6 + 3018 * q^9 + 252 * q^10 - 26448 * q^11 - 27234 * q^12 - 43488 * q^14 + 32767 * q^16 + 21762 * q^18 - 119452 * q^19 + 130806 * q^20 - 6049 * q^22 - 83379 * q^24 - 1312502 * q^25 - 94428 * q^27 - 32772 * q^28 + 735060 * q^30 + 308907 * q^32 - 1249812 * q^33 - 188203 * q^34 - 1410345 * q^36 + 353415 * q^38 - 477876 * q^40 - 1612476 * q^41 - 39360 * q^42 + 220508 * q^43 + 1082496 * q^46 - 3515619 * q^48 + 9882514 * q^49 - 136947 * q^50 - 2358786 * q^51 + 1089018 * q^52 - 8083005 * q^54 - 1285266 * q^56 - 2070294 * q^57 + 1295022 * q^58 - 8748744 * q^59 - 3070044 * q^60 + 16058050 * q^64 - 6 * q^65 - 19546374 * q^66 + 3851300 * q^67 + 10545975 * q^68 + 979920 * q^70 + 12593427 * q^72 - 9731236 * q^73 + 13246572 * q^74 + 8347746 * q^75 - 4009903 * q^76 - 9123732 * q^78 - 6855198 * q^81 + 21020522 * q^82 - 14348826 * q^83 + 44644836 * q^84 + 80099985 * q^86 + 10463891 * q^88 + 7437678 * q^90 - 3294180 * q^91 - 57890184 * q^92 - 1609122 * q^94 + 69780834 * q^96 + 9938888 * q^97 - 16049670 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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